The surf is what you see when you stand on the beach and look at the ocean — waves rising and breaking on the shore. It’s also what you do when you ride those waves. Surf’s up, dude!
Surf means "crashing waves," but it's also a verb meaning to ride those waves with a surf board. When you surf, you stand upright on a board and ride over breaking waves into the shore. A more figurative meaning of surf is "search casually," as in "channel surf," or click idly between TV stations. The origin of the word is a mystery, though it's thought to have first been used in reference to the Indian coast.