Well it could be an exercise in humility but it is also an exercise in saying "I'm sorry", which is the hardest thing in the world for people to say. That's my belief, that's why when I give you the three magic phrases I say, "please, thank you and I'm sorry". I don't say, "please, thank you and I love you", I say, "I'm sorry". It is extremely hard for people to say. By practicing it in a general way it makes it easier to say when you really need it.
Now as far as the monks go, hopefully they're not doing anything they really have to apologize for anyhow. So when they actually say it, they're trying to cover ground in case something was done unmindfully that they don't even know about. So it is a real apology in that sense, but they're apologizing in case there was anything that they did they don't know about which happens quite often. We do something but we don't realize that it actually hurt somebody. But how quick are we to apologize? Or, what often happens I'm sure for many of you, you do something wrong you didn't realize, then someone comes along and says, "Hey, you know, that's wrong", and you immediately say, "oh no, but I was doing this and no, no..." and you immediately make an excuse for yourself. How often does it happen? I'm sure it happens for many of you.
The mind doesn't want to say sorry, even though it's an easy thing to do because you actually didn't know it was wrong. Can we just come out with, "Oh, I'm sorry about this, I didn't realize it"? If we do that really quick, it's over, it's done. But if we immediately start to defend ourselves, going, "oh, but I was too busy with something else...", then we're never getting that word sorry in there to begin with. So the other person thinks we're a bit of a "you know what" and you're going to hold on to it a bit. You might think, "How dare they say I did something wrong, I didn't know it was wrong, how dare they say..." Now the point is you did something that was wrong, why not say sorry for that, too, no big deal. The more you learn how to say, "I'm sorry", the happier your life is going to be.