A macro lens can focus on things that are really close together.
How close? (Enlargement ratios explained)
A 1: 1 magnification means that a lens can focus on an object that is so close that its image on the film / sensor is the same size as the subject itself. So you can imagine that the lens is about as close to the lens as the lens is long (depending on the lens design). A lens with a magnification ratio of 1: 1 or larger is clearly a macro lens. To give you an idea, with this zoom level you should get close enough to a 50-cent coin to fill the frame, and still focus on it.
As with all lenses, the closer you focus, the closer the depth of field becomes. Macro photography is often characterized by a very shallow depth of field, creating a strong blur in the background (blurred background).
Macro lenses not just Make macro
Macro lenses are designed so that they can focus in the vicinity. However, this does not mean that they can not focus too much, and they can also serve as a portrait lens. With a few exceptions, they can concentrate to infinity. You do not have to be used for the actual macro photography (that's something I never knew when I was SLR newbie).
Properties of macro lenses in general
A macro lens of similar quality and design is usually more expensive, as its ability to focus so close requires some design considerations. It can also be a bit bulkier. However, it can provide better picture quality in some ways, and not just in macro shooting. These are just generalizations and every lens will be different.
Lenses for portrait photography
As mentioned above, macro lenses can sometimes also be used for portrait photography. Often available in focal lengths that would be of interest to portraiture photographers, they are often high quality, low distortion, fixed focal length lenses.
Traditionally, portrait photographers tend to minimize perspective distortions ("big nose effect"), so they tend to choose longer and shorter focal lengths and stand farther away. For this reason, 100mm / 105mm and 135mm primers are popular focal lengths for lenses marketed as "portrait" lenses. However, this does not mean that you only use 35mm or 300mm for a portrait, you want to reach.
This is an example of a macro lens that is suitable for portraits.