What is a blitz? In the simplest terms, a blitz is a play where the defense sends an extra player or players to rush the quarterback.
What do you mean by extra? This is when things can get a little bit complicated. In every standard defensive formation, there are players that are trying to rush the quarterback in every play. A "blitz" occurs when the play sends extra players to rush the quarterback. For example, in the 3-4 defensive formation below, there are 3 linemen and 4 linebackers. In this formation, all the defensive linemen and at least 1 linebacker are always trying to get to the quarterback, so a "blitz" only occurs when 5 players (i.e., an extra linebacker) rushes the quarterback.
What's a zone blitz? A zone blitz occurs when a defense tries to trick the offense by switching up the roles of some of the defensive linemen. Instead of rushing the quarterback every time, one of the defensive lineman might fall back to defend against passes. This might confuse the offensive lineman who is supposed to be blocking him and allow one or more linebackers through to rush the quarterback.