This meme is pretty self-explanatory. Lots of people get these two terms mixed up, but there is a distinctive difference.

Authentication is basically showing credentials (i.e., typing in a password, flashing an ID). Authorization is the next step, where it is determined whether or not those credentials are valid, and for what (this password grants the user read rights, but not edit rights. The ID, upon closer examination, says the wielder is actually underage).