The מנהג has already become widespread in all Jewish communities that we blow 100 blasts. They have relied, for this number, on the 100 cries that סיסרא's mother cried over her son. (שופטים ה) It was known to the חכמים as a tradition that the number of her cries was 100. דבורה sings about סיסרא's mother. מבעד" החלון נשקפה" until "תשיב אמריה לה" is 101 letters that contain the cries and wails of סיסרא's mother who was in pain over the loss of her son. The rest of the dialogue there is not words of pain, but rather of consolation.
What has one to do with the next? Why did they not set up the number to be 101 like the amount of her cries? [1]
The answer is that the sound of the שופר inspires mercy on the descendants of יצחק who was bound like a ram on the מזבח, whereas all the cries that סיסרא's mother cried were cries of cruelty, a cruelty the likes of which is difficult to find any place else in the entire world. A mother who is crying over the loss of her son should know the pain of other mothers who are also crying over the loss of their sons. But she was not like that, and all of her consolation was "certainly he is busy dividing up the spoils of war". This is how she mitigates her pain.
The 100 sounds of mercy made by the שופר should counterbalance the cries for סיסרא's mother that were full of cruelty, except for one, which is the pain that a mother has over her son. That one cry of mercy the sound of the shofar is not מבטל.
Therefore, the 100 sounds are corresponding to the 100 cries of cruelty.
[1] Yemenites do not blow 100 sounds, based on the opinion of the רמבם.
ספרדים indeed do blow 101, in that they add a תרועה גדולה (what אשכנזים refer to as תקיעה גדולה) at the end of davening: either before עלינו or after, which also doubles as a formal end to the service (similar to the תקיעה גדולה blown at the conclusion of נעילה). This number is the gematria of מיכאל, the intention being to strengthen his ability to defend כלל ישראל. (A full treatment of מיכאל's role in defending כלל ישראל is beyond the scope of this article, but see מדרש עשרת הדברות אות ו where he is referred to as such, being described as a כהן גדול who offers the souls of the righteous as קורבנות on the Heavenly מזבח. See also מדרש לקח טוב שמות כג:כ where he is identified as the מלאך who protected כלל ישראל in the מדבר. He is also charged, as per מלבים ישעי' ו:ו with bringing נבואה to נביאים, and keeping track of all the מעשים טובים that every Jewish person does.)
Another reason for blowing an extra תרועה גדולה is to confuse the שטן so that he does not prosecute against the כלל ישראל for going home after davening to eat and drink as though they have no fear of judgment.
Adapted from 'ספר התודעה (אליהו כי טוב) פרק שני 'מאה קולות
