A simple lens (like the lens in a pair of glasses) forms an image at a distance of f behind the lens for an object at infinity (where f is the focal length). The same lens will form an image at 2f behind the lens for an object 2f in front of the lens. This will achieve 1:1 magnification, i.e. the definition of macro. Thus any single element lens is a macro lens when mounted in a tube 2f from the sensor.

In a multi-element lens (i.e. a camera lens) the lens forms a macro image 2f behind the rear principal plane for an object 2f in front of the front principal plane. The minimum focus distance of a "regular" lens can be increased by moving it further from the sensor, using extension tubes. Thus it's tempting to say any lens is a macro lens when mounted the correct distance from the sensor (and thus there's no difference between a macro lens and "regular" lens, other than the length of tube connecting it to the camera).

However the front principal plane can be inside the lens, so for some lenses the required 2f distance from the front principal plane can end up being a point inside the lens - which is something of a problem! So a macro lens is just a regular lens with the front principal plane within 2f from the front of the lens and rear principal plane 2f - ffd from the rear of the lens (where ffd is the flange focal distance).

The position of the principal planes in a multi element lens are highly influenced by the distribution of positive and negative elements in the lens. A retro-focus design, commonly used by wide angle lenses, pushes the principal planes backward, whereas a telephoto design pushes them forwards. This is the reason you tend to see many more telephoto macro lenses than wideangle macros.

In addition to the position of the principal planes, macro lenses are usually optimised to have a flat field i.e. the focussed image is planar as opposed to slightly curved. This is not a requirement for a lens to be a macro, but a useful feature of lenses used to photograph flat objects at close distances, e.g. to copy documents.