Wanna and gonna are contractions for "want to/a" and "going to," respectively. They are informal and usually used in spoken English but not written English.

Steven's answer is correct. They are both understandable but very colloquial. You should avoid using them, unless you intend to be very informal e.g. when sending a text message, for the sake of speed.

Steven answered the question already. I just want to add that the reason these words exist is because of how quickly native speakers speak the language. It takes more time to slow speech down to fully pronounce "want to" and "going to" than it does to just slur through and say "wanna" and "gonna." The same can apply to "kinda" and "sorta," which are contractions for "kind of" and "sort of" respectively. Although none of these contractions are considered proper in any standardized versions of English, they're perfectly okay to be used when communicating casually (such as when texting with a friend).