Why do Christians listen to so many sermons? Is it a matter of filling their minds with lots and lots of information?

Well, yes, but that's not the main purpose.

I've been listening to a talk on expository preaching by John Hosier, in which he quotes Martyn Lloyd-Jones as quoting Jonathan Edwards as follows (so you are now reading Anthony Smith on John Hosier on Martyn Lloyd-Jones on Jonathan Edwards on preaching):

The main benefit obtained by preaching is by impression made upon the mind at the time, and not by an effect that arises afterwards by a remembrance of what was delivered. And though an after-remembrance of what was heard in a sermon is oftentimes very profitable; yet, for the most part, that remembrance is from an impression the words made on the heart at the time; and the memory profits, as it renews and increases that impression.

Martyn Lloyd-Jones comments:

The first and primary object of preaching is not only to give information. It is, as Edwards says, to produce an impression. It is the impression at the time that matters, even more than what you can remember subsequently.

Preachers: don't give a lecture! Listeners: let the words sink into your mind—and through your mind to your heart—now; don't just scribble them down to think about later!