Difference between cross breeding and hybridization?

Crossbreeding is the mating of two individuals within the same species. A Labradoodle is a crossbreed of a Labrador retriever and a poodle -- both dogs.

Hybridization is the same as cross-breeding, but is often deliberate, with the objective of an increased chance of desirable characteristics.

A hybrid is the result of mating two different species. A mule is the best-known example - it is the offspring of a male donkey and female horse (the offspring of a male horse and female donkey is called a hinny). Only closely-related animals can breed - usually they must be in the same genus (like horses and donkeys, which both belong to the genus Equus), and at the very least they must be in the same family. Even then, hybrids are usually sterile, a result of the parent species having different numbers of chromosomes. You can also call a hybrid a cross - e.g. a mule is a cross between a donkey and a horse.

I think habiba's answer is more accurate. Hybridization should be the breeding between two individuals from different species.

Cross breeding on the other hand, is like emhen said is mating of two individuals within the same species, but who belong to different breeds.