To snog is to kiss. A teenage couple might snog throughout an entire two hour movie.
The verb snog is British slang for kiss, cuddle, or make out. It's a word that is more and more common in American English as well, as a casual way to talk about kissing. It can be painful for kids to watch their parents snog, and many of them don't want to see people snog in movies either. The word has been around since about 1945, though its origin is unknown.