Democrats hold that the government should take care of its people. They tend to believe more in "big government" programs, such as national health care. They tend to support more socially liberal policies.
Republicans hold that the government should be the framework, but the work should be done by individuals. They also tend to support states rights over federal. Also, they tend to be more socially conservative.
Both parties want to help the poor. The Democrats want to redistribute the wealth of individuals so that the poor get more aid. Republicans tend to focus more on business, to provide jobs for the poor to take care of themselves.
Nothing is black and white of course, But I tried to give a balanced view of the differences as I see them.