There are generalizations for each; some are more accurate than others.
Republicans are considered on the "right" end of the political spectrum while Democrats are on the "left." The far right generally is pro-religion, anti-bureacracy, pro-military, pro-business and pro-personal responsibility.
To the far left of the spectrum are the extreme liberals, or the most extreme democrats. Everyone pays taxes to equalize society. Government should solve all problems and government should be counted on by people who can't take care of themselves. Republicans might see this is bordering on communism.
Republicans, are usually considered conservative (fiscally as well as socially), maybe a litte pious, pro-business and against the bureacracy often associated with big government. They see big government as wasteful and an obstacle to getting things done. Their approach is very Darwinistic in that the strong shall survive, cream rises to the top, etc. And the weak become Democrats so that they can get handouts from the government. Work hard, obey God and life will be good. In theory, this is a neat way to look at things and in an ideal world, this would be great, but it has a number of flaws.
Democrats are considered more liberal. They are usually more educated and open-minded. . . maybe a little more realistic; maybe a little more cynical, depending on how you look at it. Democrats often come from in or around an urban area and have more exposure to the realities of a life for those with diverse backgrounds. Thus the likelihood of social liberalism among democrats.
Republicans expect people to take advantage of the fact that we are in a free society and, as such, they should take advantage of this opportunity to make wise, responsible decisions for themselves, which should ultimately trickle down and result in a better society.
Democrats are smart enough to know that most people don't always make the best decisions for themselves (or society) so their position is that there needs to be more regulation, thus a more structured government. This is kind of along the lines of Hillary Clinton's famous statement that "it takes a village to raise a child." The village, many would say, is the government.
Republicans will say that Democrats want to increase taxes (and the size of government) in order to pay for wasteful social programs. Republicans would rather funnel the money to churches and charities so that the government can be left to do what it does best. Let the churches and charities take care of their communities. Let the government take care of law enforcement, defense, etc.
Democrats will say that Republicans don't care for anyone but themselves (who are often in the higher echelons in terms of income) and that Republicans should share more of their wealth with society.
But there is a ton of hypocrisy and an incredible amount of contradiction in both parties. Both parties are right. And both parties are wrong.
Bottom line, as an earlier poster explained, people are going to support the political parties that are known to best serve their own, individual needs.
Low income urban minorities are more likely to support a Democratic agenda because it's in their best interest.
Middle and upper class rural citizens (whites and minorities alike, in many cases) are more likely to gun for Republicans because their agenda is friendlier to these types of citizens.
When voting, your best bet is to vote based on the individual candidate as opposed to the party with whom she or he associates.
And it's your responsibility as a citizen to educate yourself so that you can make informed decisions.