While there are many technical definitions of what makes a macro, the simplest explanation is as follows. Macro photography is the art of making tiny things look big. You can do this by getting very close to your subject, or by getting a telephoto lens and zooming way in.
Macro photos can be of pretty much anything, but there are some classic genres that macro photographers come back to again and again. Insects are the perfect example. They are tiny, and a great macro image of an insect takes the viewer into an entirely different universe.