I don't think there is any one thing that defines them.  You don't have to figure out which one.  If you really want to pick one, it's basically a matter of which you has more philosophies and policies you agree with.  Democrats tend to be more inclined to spend money on social services and impose taxes on the wealthier portions of society to pay for it.  Republicans tend to favor private businesses as a means of aiding the impoverished portion of society, and consequently often advocate lower taxes and reduced spending.  However, there are always exceptions, and there is a huge range of variation within the parties (people are going to object to this - lets just say it's signficant relative to the total variability and mainstream American politics).  If you identify with more one party or the other that's fine, but if not, you don't have to choose.  And whatever you do, don't vote for a bill or a candiate just because your party supports it/him/her.  Vote for it becaues you think it/he/she is a good bill/candidate.  Whatever you decide is fine, just make sure you're deciding for yourself!