There are some good long answers already, so I'm going to try to give as short an answer as possible.

A quantization of X is some X_hbar depending on a parameter hbar (ocassionaly q=e^hbar instead) such that X=X_0 and X_hbar is generically "less commutative" than X.  This is by analogy with quantum physics where X_0 is classical physics and hbar measures the failure of position and momentum to commute.