It's a way to end a conversation. One might also say, "I need to get going."

It's like a polite way to say I am starting to feel awkward and feel the urge to leave. As far as a synonym goes I can not think of a another way to say it besides "I feel awkward and feel like leaving would be best." Saying "I am getting going" sounds like someone told you to leave and you were being submissive to their command. It would be more ear pleasing to say "I am going to go (now)."