Cartoon is a style of art started, depending on who you talk to, by a whole list of groups, including the Mayans (see Understanding Comics by Scott McCloud), as a form of social protest in the American Colonies in the 1700s (see Drawn and Quartered by Stephen Hess and Sandy Northrup), or, popularly, in the late 1800s/early 1900s by newspapers trying to increase their popularity (see The Yellow Kid, the Katzenjammer Kids, Little Nemo In Slumberland).
The art style has a few different branches of "sub-styles" so to speak, but is generally known by the following: characterization of the human figure, surrealistic characters (including everything from anthropomorphic animals to dieties of all sorts), and the coupling of stories/implied stories with these artworks, usually creating sequential artwork of some kind.
Many different types of artwork are called "cartoons" - from comic strips, to animation, to comic books, to illustrations, to greeting cards. It's kind of a misnomer, but popularly the word "cartoons" in America referrs to animation, comic strips or omic books.
All of these types, oddly, have their own individual quirks which make them quite different: comic strips, for example, usually are humor-based stories, with the figures usually being characterized in ways to make the figures appear more child-like and friendly. They also almost always include wording contained in word balloons. Comic books, though, usually use more realistic figures, exaggerated usually to show larger/more powerful bodies, and have more serious stories. They also are in a book format, released usually monthly, as opposed to the daily format of comic strips. Animation, on the other hand, is a completely different beast, using the styles above as a basis, but portraying these on film instead.
Many of these sub-styles cross over one another, there's a lot of activity by individual artists of varying types, from super-realistic to extremely suggestive symbolic representation, and examples which borrow from one another (and everything else under the sun) are quite common.