No real difference between the two, other than as a way to narrow down which candidates you get to choose during the primary elections (the elections to determine who your candidate will be for the next election for office).
Traditionally, the Republicans have been pro-business whereas the Democrats tend to be more oriented on social issues, such as welfare, education, and social services. The distinctions tend to get a little blurry, and its common for a folks registered as a Democrat to vote for a Republican candidate.
Its a lot like trying to explain the difference between a Miami Dolphins fan and a New York Jets fan. Both love football and think the other team's fans are evil.