רבי יהושע בן לוי used to gather his family members and read the מגילה to them [1]. Based on this, people are נוהג in some places to bring children to hear מקרא מגילה, in order to be מחנך them in the מצוה of פירסום הנס [2]. This is why the congregation is נוהג to say certain פסוקים out loud, namely איש יהודי ,ומרדכי יצא, ליהודים and כי מרדכי (specifically those because they are the primary beginning and end of the נס), in order to wake up the children that they shouldn't fall asleep but rather that they should pay attention to the reading, to which end we are מקריא those פסוקים to them to train them [3].
One should be careful, however, only to bring children to shul if they are mature enough to sit through the reading quietly, or else they may disturb the rest of the audience [4].
The above is all in the past. Today, however, it is נהפוך on account of our many sins, in that not only do children not listen - but they even disturb so much as to prevent the adults from listening themselves, the only reason they come to shul in the first place being to bang המן, and if that is the only reason they come to shul then a father does not even fulfill his מצוה of חינוך at all. Really, as far as חינוך is concerned, every father has to hold on to his children and supervise them to make sure that they listen to the reading, and where the בעל קריאה mentions 'המן האגגי' then the child can bang as he normally does, but that banging should be the main purpose of bringing a child to shul in the first place is misplaced emphasis [5]. Not only that, but today it is a good idea for everyone to have a מגילה כשרה and read every word quietly with the בעל קריאה, because otherwise it is often impossible to hear anything on account of the noise that people make with their sticks [graggers?], and anyone who has the ability to do should do so. If a person does not have a מגילה כשרה - one should then at least read along quietly from a חומש [6]. Women should also have a מגילה כשרה from which they should read quietly to themselves, as often in the ladies' gallery it is even more difficult to hear the בעל קריאה than it is in the shul, on account of all the noise [7].
Addendum
The precise לשון of the מחבר [8] is that bringing children to קריאת המגילה is a ''מנהג טוב". The מחבר is clearly referring to children that are הגיע לחינוך, because, after all, smaller children are only likely to disturb, in which case why would bringing children who are הגיע לחינוך to shul be called a מנהג טוב and not a חיוב if, after all, מדין a father is obligated to train them in קריאת המגילה? Perhaps for that it would be enough to read for them at home, but in order to publicize the נס more, there is therefore a מנהג to bring them to shul so that they get used to hearing the מגילה being read בציבור [9].
[1] ירושלמי מגילה ב:ה
[2] טור או"ח תרפט:ו, לבוש שם
[3] לבוש שם
[4] מ"א שם ס"ק יא, ערוה"ש שם סעיף ג
[5] מ"ב שם ס"ק יח
[6] שם ס"ק יט
[7] כה"ח אות כז
[8] שם סעיף ו
[9] ביה"ל שם
