Induced fit or conformational selection seems to be the two explanations with the most backing.

In induced fit, binding of the ligand changes the shape of the protein.

In conformational selection, the protein samples a number of different shapes, a subset of which is compatible with ligand binding.

I tend to think that "induced fit" is essentially conformational selection. All molecules seem to "breathe" to an extent, ie. small-scale movements between atoms (you can see this on structures in PyMol by looking at the B-factor) so this makes the most sense.