If you cut a player you lose rep, but not prestige? which one factors into recruiting?  What does rep do?

rep may play a small role in recruiting, but I haven't noticed very much effect (though I've never had a bad rep, just from observing a few others who had less than spotless reps).  Your prestige is far, FAR more important in recruiting.  Rep is important when trying to move up a division.  You can actually be blocked if your rep is bad enough.

Your reputation is how you are viewed as a coach. Factors that may impact your rep include - recruiting violations, rescinding a player's scholarship that you didn't recruit, breaking promises, having a player quit, and/or having a player declared academically ineligible.

Prestige is how your team is viewed relative to other teams. Your coach rating can have an effect here. For example, when changing teams you might take over a team with a C prestige but that could possibly change to a C+ or C- depending on your prior success and experience. As jdno said, prestige carries far more weight in recruiting than reputation.