Technically, Macro is when the image projected onto the recording medium (sensor or film) is the same size or larger than the subject, so a rectangle measuring 36mm x 24mm taken in true Macro will fill a Full Frame sensor (or 35mm film frame) completely. Some lenses are called Macro incorrectly - they can just focus closer than the non-Macro variants. Wikipedia goes into more detail but the above is (I think!) a fairly basic and accurate answer. HTH.
This is a rigorous and widely used definition of "macro", but it has an implication that limits its practical usefulness somewhat in my mind at least.
Suppose the same scene is photographed with several cameras which have different sized sensors (a spider on its web for example, showing exactly the same amount of the web in the photo from each camera), for example a full frame camera (with a sensor 36mm across), an APS-C camera (sensor about 22mm across) and a super-zoom bridge camera (sensor about 6mm across).
If the scene is 30mm across it will be macro when photographed with the full frame camera but not the other two.
If a smaller scene is photographed, say 20mm across, it will be macro when photographed with the full frame or APS-C camera, but not the bridge camera.
Not until a scene is photographed which is 6mm or less wide will it be macro on the bridge camera. To put this in context, on a full frame camera a scene 6mm wide needs a magnification of 6:1. This is so much magnification that you can't achieve it on a full frame camera when using the extremely powerful Canon MPE-65 macro lens, which goes to a maximum of 5:1 magnification.
I deal with scenes of varying widths, some less than 10mm wide. Most are taken with a super-zoom bridge camera and strictly speaking none of them are macro, even though very many of them fall well within the range of what would be macro with a larger sensor camera.
I refer to my photos as close-ups to avoid arguments about whether they are "really" macros or not.