"What's up?" is a way of initiating an informal conversation. It's a way of asking what's new with you. You can reply by saying what you've been doing lately or at the moment. Example replies: "I'm just doing some shopping"> "I'm just relaxing". Or if you don't have anything new to say, you can reply like this: "Not much. What's up with you?"

"Not much. What's up with you?"

As the others' excellent answers say, "What's up?" is a greeting. It is also a question. If someone sees you upset or angry, they may also ask "What's up?". Here it means what is affecting you? What is bothering you? . Regarding the greeting: The often-used answer of "Not much" is a trap, I feel. The greeting is to start a conversation. Unless you want them to go away thinking you are boring, use the opening. Tell them what you are going, planning, or just done. Also as the answers said, ask them too. Invite the other person to tell you.

I think a more common dialogue would go like this: Alan: What's up? Mr Wright: Not much. What's up with you? Alan: Oh, just answering some questions on italki. Mr Wright: Really?! Me too! In other words, I am saying that in most cases the greeting and response will be said before anything else is said. (And the above dialogue assumes that "Alan" and "Mr Wright" feel comfortable speaking to each other using informal phrases. Either they already know each other, or they are being introduced to each other by a friend in a context in which informal language is acceptable.)

"Nothing much. What's up with you." Notice that the greeting ("What's up?) and the response are informal in nature and would be used by friends, family members or people of the same age group (and perhaps not by people older than sixty).