I had an interesting discussion last month with a fellow prospective student, trying to figure out the nature of humility. But it may be easier to start with arrogance. The basic definition might be something like thinking that you're better than other people. But this needs finessing. No doubt you are better than many others at various particular things, and it could hardly be blameworthy to recognize this fact. So I take it that arrogance essentially involves some kind of distorted (read: inflated) self-evaluation.
There are two ways this distortion might go. The most obvious is a simple factual over-estimation, i.e. you think you're more talented than you really are. Alternatively, one might distort the normative significance of their particular talents, perhaps thinking that it makes them an intrinsically superior person. (This must be a distortion if we hold that all people are of equal intrinsic value.)
But I think it's broader than this. Couldn't someone be arrogant in particular respects -- e.g. dismissing the ideas of untrained students in their field (to adapt an example from Siris) -- without any presumption of overall superiority? There seems a close link between arrogance and disrespect, and I assume the latter can be 'particular' in this sense.
Turning it around, then, could we say that humility is simply the disposition to treat others with respect (take them seriously, etc.)? One advantage of this over "self-evaluation"-based analyses is that it doesn't risk conflating humility with low self-esteem. Plus, it doesn't require the humble person to avoid self-knowledge (regarding their talents). Any objections?