Big, insincere tears in a person are called crocodile tears. But crocodile tears in a crocodile aren't tears at all. Crocodiles have no tear ducts. (And what does a crocodile have to get all emotional about, anyway?)
What look like tears are actually glandular secretions. Unlike alligators, which prefer fresh water, crocodile usually live in saltwater marshes, which can be hard on the eyes. The crocodile produces the secretions to wash the salt from its eyes.
Incidentally, the primary difference between alligators and crocodiles - apart from these secretions, is the shape of the two reptiles' snouts, which are broader and rounder in alligators.