Gonna is the colloquial (slang) version of going to. You would never write gonna in a business or academic paper but it's said all the time. Also, gonna is used for cases that mean "will" or "about to", you would never use it to mean "going to" to mean actually leave and go to somewhere else.
Correct: I'm gonna talk to him.
Correct: I'm gonna go see a movie later.
Correct: I'm going to his house.
Wrong: I'm gonna his house.