Let me nuance what Adam said (it's not wrong, but there's an extra subtlety here). Someone's elbow might hit someone else accidentally. "Hit" just refers to the moment when the elbow touches the other person; it might not be intentional. We don't know if this person wanted to hit you with their elbow. Maybe they just sat down on the bus next to you and have very long arms. But "to elbow" (the verb) is the rude, intentional, somewhat violent action of jabbing at someone with your elbow. Of course, this involves a hit, but it adds intent: the person wanted to hit someone with their elbow: they elbowed them.

Hi guys I would like to add another 'nuance'. :-) Sometimes the verb "to elbow" is used in a phrase where a person wants to attract another person's attention to something. In this context it isn't usually violent or necessarily rude... it's normally intended to be helpful. You normally know from the context (as always!). In this case it's not really a synonym for 'hit'... I'd say 'nudge' is a better synonym in this context

Yes. That's what "to elbow" (someone) means as a verb.