I don't get it.
"I don't get it" is a way of saying "I don't understand." You say this when you don't understand something like:
- a joke
- an explanation
- why a character in a movie acted in a certain way
You probably wouldn't say "I don't get it" if you don't understand things like:
- what someone said (meaning the words, not the content)
- an entire subject, such as Physics
- something that's never been explained to you, and that you haven't even tried to understand
"I don't get it" is more casual than "I don't understand."