Inspired by my roommate calling my new acquisition abstract. I guess I'm a purist; for me abstract has to be abstract, that is, depicting an abstract concept. So I wrote this for people new to modern art...
For example, Mark Rothko
The art does not depict anything in the natural world. The artist instead uses the paint (or whatever media) to convey emotions or abstract ideas.
For example, Georges Braques
Cubism represents a real-life subject from several perspectives at once in order to get at the essence of it.
For example, Kasimir Malevich
Minimalism is only about the visual impact. It makes no attempt at narrative or expression or representation. To some people, this is the only pure art. (I'm not a fan, but there are some pieces I really love, like the one I linked to above.)
For example, Joan Miro
Surrealism may or may not depict real-world things. Most of Miro's doesn't; most of Dali's does.
From Artcyclopedia: Surrealism is a style in which fantastical visual imagery from the subconscious mind is used with no intention of making the work logically comprehensible.
For example, my new acquisition.
This is a broad term that can be applied to art from a lot of different styles and periods. Think Munch, El Greco, Van Gogh, Goya. I like the Wikipedia definition a lot: Expressionism is the tendency of an artist to distort reality for an emotional effect; it is a subjective art form. This is my favorite kind of art to look at.