Agreed with Saramehr. In starting a conversation, either in person or on the phone, it's asking 'what's new in your life?' (usually as far back as the last time we spoke or saw each other)
Common equivalents are 'what's new?' and 'what's going on?'
When two people are passing each other on the street and don't stop to talk, in AmE it's used as a simple greeting. You're not expected to actually answer with what's been happening with you recently. You can simply say back 'hi', 'hey', 'hello', another 'what's up' or even 'how's it going?" In this context, even asking 'how's it going' or 'how are you' is just a greeting if two people are passing each other and don't stop to chat.
I can think of another context in AmE, not too often heard, between two people about to get in a fight or argument. If, for example, you're in a crowded bar and you hear someone saying bad things about you, or you see someone flirting with your girlfriend (or any other kind of situation that makes you want to confront people), you could confront that other person with 'what's up?' I consider this mostly used by young guys in American 'frat boy culture'.
(not a teacher, just a language lover)