"Got it" means "I understand." You say this when someone is giving you instructions or teaching you something:

A: That piece goes over here like this, and this piece screws into the top.

B: OK, got it.

You can think of "Got it" as a shortenened version of "I've got the idea (of how that works / of what to do / etc.)"

"Got it" is more casual than "I understand." So, for example, you would use "I understand" if you were being yelled at by your boss for doing something wrong:

A: You should not have done that without checking with me.

B: I understand.