Clarification on $M^2$ factor

In beam optics, the $M^2$ factor is a "catch-all" single number that describes how "good" a beam is, i.e., how close it is to an ideal Gaussian beam, which by definition has $M^2 = 1$. This encyclopedia article says that "A laser beam is often said to be "$M^2$ times diffraction-limited"." But what does that mean? I assume it is as simple as having a beam with e.g. $M^2 = 2$ grow twice as fast in diameter, all other things (wavelength, beam waist) being the same? Or is there more to it?

On a related note, how good of a description is the $M^2$ factor in practice? The linked article talks about how a single number simply cannot describe all qualities of a beam — and I agree with that –, but would a simple description with the $M^2$ factor really be that bad?