1
The שבת before פסח is called שבת הגדול, because of the miracle that occurred on it, namely, that once the Egyptians noticed בני ישראל designating sheep (לבוש [1] even says they dragged the sheep on the ground purposely to denigrate the Egyptian idol), they then asked what the sheep were for [2] and were told that the sheep were for the קרבן פסח which would protect them (בני ישראל) from מכת בכורות. At that point the Egyptian בכורים lobbied פרעה to release בני ישראל, which he refused to do; so the Egyptian בכורים went to war against the rest of Egypt, resulting in many casualties on both sides. [3]
Alternatively, the Egyptians observed בני ישראל designating sheep. Upon inquiring as to the purpose of said sheep, they were then told that the sheep were going to be slaughtered for a קרבן פסח. The Egyptians were miraculously prevented from saying anything, so they were left only being able to gnash their teeth over the fact that their idols (the sheep) were going to be slaughtered. Being that יציאת מצרים took place on Thursday, we thereby deduce that the sheep were designated on שבת. On account of this miracle, the שבת before פסח is referred to as שבת הגדול [4].
Now, it seems a bit strange that the miracle is related to שבת before פסח rather than the day of the month, namely י ניסן. -?- The problem is that בני ישראל came out of the ירדן on י ניסן [5], so if י ניסן were to be designated a festive day then the assumption would be that it is festive on account of בני ישראל coming out of the ירדן. To avoid such misconceptions [6], the miracle of the Egyptian בכורים waging war is therefore commemorated on the שבת before פסח.
Additionally, מרים died on י ניסן, in which case the date of her passing would end up begin established as a fast; on שבת, however, one may not fast on account of a yahrzeit [7].
Alternatively, the entire miracle occurred as a result of שבת, meaning, that the Egyptians saw בני ישראל handling animals on שבת specifically, which was strange because animals are מוקצה on שבת and, as such, may not be moved on שבת. This is why the Egyptians asked for an explanation, and either of the two miracles described above then occurred [8].
A deeper explanation proposed by the ערוה"ש [9] is that שבת and יציאת מצרים depend on each other, in that שבת is a testimony to the creation of the world, and פסח is a testimony to Hashem's special attention and value for כלל ישראל. One without the other would be pointless, which is why Hashem gave us שבת immediately upon leaving מצרים, without waiting for מתן תורה, because יציאת מצרים and שבת depend on each other. This is why this שבת is called שבת הגדול, because besides for the creation of the world, Hashem's השגחה was also made clear, and we also were נתגדל by being chosen from all other nations, which is the true reason why we call it הגדול.
2.1
There is a מנהג to say the הגדה from עבדים היינו until לכפר על כל עוונותינו by מנחה on שבת הגדול (at which point those who otherwise say ברכי נפשי stop doing so) [10]. The reason for this מנהג is because the גאולה started from the point where the sheep were designated for קרבן פסח [11]. This is done even where ערב פסח falls on שבת, in which case the דרשה (which will be discussed shortly) is rescheduled for the prior week [12].
There is also a (to my knowledge) universal מנהג that the rabbi addresses the congregation on matters pertaining to פסח (known as the 'שבת הגדול דרשה'). In some communtities, the rabbi takes this opportunity to teach הלכות פסח. In other communities, it is assumed that anyone who has a shaila will ask the rabbi directly and individually [13]. To that end, some rabbis take the opportunity to exhort the congregation to destroy the חמץ of their crooked actions, confused ideas, and rotten מדות [14].
On account of these two מנהגים, some say this is where the designation of שבת הגדול comes from, namely that people spend so much time in shul hearing all the הלכות of פסח and relating the miracles and wonders that Hashem did for our ancestors in מצרים that the day seems very big (in length and/or in prominence), which is why it started being called שבת הגדול [15].
2.2
מדקדקים are נוהג that instead of saying ומבורך שבת שלום or גוט שבת as they would normally, they instead say שבת הגדול מבורך or א גוטטען שבת הגדול [16].
2.3
At one point, all of כלל ישראל had a מנהג to bake bread on ערב שבת הגדול to distiribute to the poor, and from the day that people were מזלזל in this מנהג - there was then a curse against the grain [17].
3
The deeper message of שבת הגדול
Adapted from the שבת הגדול דרשה of ר משה Feinstein delivered in 5682
שבת is the תכלית הבריאה, the pinnacle or peak for which the world was created [18], because if not for שבת then a person would hardly have any opportunity to contemplate spiritual matters, so by keeping and remembering שבת - a person then comes out of the גלות spiritually thereby; even if the body is in גלות, still the spirit is not in גלות in that it has no master other than Hashem. In מצרים, where the תורה was not yet given such that the spirit was still in גלות - the מצוה of קרבן פסח was therefore given to us to be eaten בחבורה and to the exclusion of בני נכר, and even a ישראל whose actions were נתנכר from הקב"ה (i.e. an ערל - ed.) is not fit to eat the קרבן פסח, and with this (the fact that the קרבן פסח could only be eaten with non-ערלים) the spirit already had its redemption through the תורה. But after מתן תורה where the spirit was already redeemed by means of the תורה from which point the spirit is no longer נשתעבד - then even though the body is in גלות, still the נפש is not in גלות, and that is by means of שבת which enables the נפש to contemplate properly. So by means of the קרבן פסח - a person thereby reaches a recognition that the primary גאולה is that of the spirit and the soul through קבלת התורה whereupon the spirit is no longer נשתעבד. This is the deeper meaning behind why this שבת is called הגדול: because at that point בני ישראל recognized the גדולה of שבת and its position as the תכלית הבריאה.
[1] או"ח תל:א
It is worth noting that בני ישראל were not previously aware that the Egyptians would be prevented from doing them any harm; rather, they placed their full trust in Hashem that no harm would befall them from doing a מצוה.
(מ"ב שם)
[2] פרישה (ס"ק ב על הטור שם) specifies that what the attention of the Egyptians was that they saw בני ישראל making knots. Since they knew that tying a knot is אסור on שבת (but they didn't know that a temporary knot is allowed), they therefore asked why בני ישראל are suddenly tying knots. -?- To which they responded as in the main text.
What puzzles me, however, is why the Egyptians would notice the knots more than the sheep. -?- Additionally, פרישה does not bring any source to the effect that בני ישראל were vigilant about the איסור of tying knots on שבת at this point in their history (i.e. before they received the תורה). וצ"ע
[3] This is the meaning of למכה מצרים בבכוריהם (תהלים קלו:י).
תוס' שבת פז: ד"ה ואותו יום
[4] טור שם
A slightly differing account if given in כל בו סי' מז, to the effect that the Egyptians actually wanted to annihilate בני ישראל on account of their slaughtering sheep, so Hashem therefore plagued the Egyptians with various illnesses, thus disabling them from hurting בני ישראל in this instance.
[5] יהושע ד:יט
מלבים there points out that the פסוק specifies what day of the month it was that they crossed the ירדן to demonstrate that there wasn't simply a tidal recession (what he calls 'ebb and flow') that יהושע calculatedly took advantage of - as the cynics would have it; rather, the drying of the ירדן was completely miraculous.
Presumably, though I have not found this point made directly in any source, the reason why one would automatically assume that י ניסן is festive on account of the ירדן rather than יציאת מצרים is because the date of the crossing of the ירדן is explicit in a פסוק, whereas the chronology of יציאת מצרים is only deduced by חזל, making the crossing of the ירדן more obvious to anyone who learns נביאים.
[6] One might wonder what the major problem is if there will indeed be a misconception. -?- There is to say that we pin these days on the miracles of יציאת מצרים, which are of greater significance than the miracles related to the crossing of the ירדן.
ע"פ ערוה"ש שם
[7] עיי"ש שקבעו כעיקר, וכמדומה שראה את פשט זה בשום ספר. וצע"ק דהא איסור מוקצה הוא או הלכה למשה מסיני או תקנת נחמיה בן חכליה כדאי' בערוה"ש תחלת סי' שח באו"ח, ומהיכן ידע שהיה איסור מוקצה קיים אף קודם מתן תורה. ושם כתב כי בודאי היו שומרים שבת ממסורת אבותיהם, אבל עדיין לאו דוקא שהיה להם איסור מוקצה ג"כ
[8] מור וקציעה שם. The תענית referred to here is one of a list of optional תעניות listed in שו"ע או"ח תקפ:ב.
[9] שם סעיף ד
[10] רמא שם סעיף א
[11] ביהגר"א שם אות ב, [וכך אי' במעשה רב קעז] ועיי"ש שפסק שמנהג זה אינו נכון, שהרי מצות סיפור-יציאת-מצרים היא רק כשמצה ומרור מונחים לפניך, כדאי' במכילתא סוף פרשת בא. אבל לי הקטן אין זה מובן, כי אין מנהג זה לשם חובת-מצות-סיפור, אלא רק למנהגא בעלמא. ואפשר כוונתו שמנין לנו להוסיף על המצוה [ונתקשה בזה במור וקציעה ג"כ], אף בדרך מנהג בלי חובה גמורה
וראיתי מובא [שערים מצויינים בהלכה קז ס"ק ה] שהיו צדיקים שעשו פשרה דהיינו שאמרו רק את החרוז הראשון בכדי שלא לבטל את המנהג ותו לא
ובאשכנז נראה שלא אמרוהו כלל, כדמשמע ממנהגי וורמז [של ר' יוזפא שמש אות עב] ששם כתוב "ושאר המנהג (כלומר לבד ממה שפורט שם אחרת) הוא ככל שאר שבתות השנה", ומנהג זה לא הוזכר כלל. גם במנהגי וורמז לר' יודא ליב קירכהיים ובמנהגי אמסטרדם ליתא.
ומהריץ הלוי נהג לאמרו יחד עם בני ביתו באותו ניגון שבו אמרו את ההגדה בלילות הסדר. כך נוהג הרב שמואל קמנצקי (שמעתי מתלמידו מו"ר הרב דניאל אשר הכהן קליינמאן)
אבל בשנות רבנותו בלונדון היה אומר את ההגדה בציבור אחרי תפלת מנחה קודם עלינו לשבח, ואח"כ אמרו קדיש יתום, עלינו, עוד קדיש יתום, ואח"כ הדרשה. (מנהגי מהריץ הלוי פרק ו אות ח)
[12] חק יעקב ס"ק א שם
[13] ערוה"ש שם סעיף ה
[14] כף החיים שם ס"ק ד
In the Syrian community, this was historically about one and a half hours long, consisting of three parts focusing on גמרא, הלכה and אגדה respectively. (Rabbi Herbert C. Dobrinsky, A Treasury of Sephardic Laws and Customs, Ktav, 1988, page 253)
While R. Joseph Hirsch Dunner was a rabbi in London, he would break up his דרשה into two parts: the halachic-ethical section, which was geared towards the general public, he would say after קריאת התורה before מוסף, while the פלפול section, which was geared towards לומדי תורה, he would say after מנחה while wearing a טלית over his head (presumably this was done לכבוד הציבור - ed.). The latter section was based on a series of sources which would be publicized in advance. Sometimes, at the end of the פלפול, he would exhort the audience about communal matters that needed attention or improvement. (מנהגי מהריץ הלוי פרק ו אות ז)
"It behooves the members of the community to be present at this important event. This brings honor to the Rav and also to the occasion." (Rabbi Dovid Ribiat, The Halachos of Pesach, Misrad Hasefer, 2020, page 83)
[15] מטה משה תקמב
[16] ע"פ מחזיק ברכה או"ח שם אות ב
[17] כף החיים שם ס"ק ה