A macro lens is a lens that you can use to protograph on a relatively short distance, to take extreme closeups.
For a short focal length, that means as close as a few centimeters, for a long focal length it can be several decimeters.
The classical definition is that the image on the film plane should be close to, or larger than, life size. With digital cameras with smaller sensors it's hard to reach that definition, so some manufacturers uses the definition that a regular 10x15 cm print should be close to life size.
There are special macro lenses, but you can also use a extension tubes or close-up lens to give a regular lens macro capabilities.
Examples of macro photos; a bottle neck and a rowan flower. Notice the blurry background, which is common for macro photos as the background is so far away compared to the subject: