You'll have to check your school's music web site and look at the audition requirements there (they're almost always online these days). Different schools have different requirements. For example, at one university nearby, they want you to be able to play scales up and down 4 octaves and memorize 4 pieces from all 4 eras of classical music for the audition. Another school only wanted 3 octaves and 3 pieces.
Generally, you'll want at least one piece of music from each era of classical music - baroque, classical, and romantic, or even contemporary. The safest choices are almost always Mozart, Chopin, Bach, Beethoven... I auditioned at a university after only a year of lessons with one piece each by Mozart, Bach, and Beethoven, and passed it.
You will want to have them memorized, ideally. That's a major plus, as is playing the pieces cleanly. If you're wanting to enter as a performance major, the judges will be even more critical of your playing - you will have to play very clean, from memory, and emote a lot. They're a little more lenient with therapy/composition/education/etc. majors.
As for the characteristics... the universities I've looked and auditioned at had no requirement for the pieces other than what I've already discussed. Though, it probably wouldn't hurt to prepare a set of pieces that contrast with one another - one happy, one sad, one in between, that kind of thing.
In the end, though, just check the websites of the schools you are looking at. You should find all the audition requirements and suggestions there!
EDIT: They may also ask you to sightread something, though I never had to deal with that (even though it was on the audition requirements!). Generally after a couple of scales and your prepared pieces, the judges will be able to get a decent idea of your abilities without spending much more time on anything else.
Topic: Pieces requested for an audition