Quantum mechanics, no one will be surprised to hear, is weird. In particular, photons can carry angular momentum - circularly polarized light can set objects spinning. But it turns out that light can carry orbital angular momentum as well. It's really not very clear to me quite what this means in terms of photons. In terms of classical waves, it's weird but I think I get it: if you look at the spatial distribution of the light in a beam, you may find that the phase is constant across the whole beam. But you might also find that the phase varies. Now, it has to be continuous, but you can imagine that as you make a circle around the beam center, you find the phase increases by an integer multiple of two pi. This gives you a continuous phase in a way that is topologically different from the constant-phase situation. As I understand it, this is what is called wrapping number.

Now this would just be another weirdness from the world of (classical!) waves except that there seem to be applications for it. In particular there's a paper on the arxiv about using this for communications purposes.