Allow me search it for you, here it is...

surf - a whatis definition

In using the World Wide Web, to surf is to either:
1) Explore a sequence of Web sites in a random, unplanned way, or
2) Simply use the Web to look for something in a questing way.

As the term is ordinarily used, if you are going to one specific site you already know about, you aren't surfing. The term suggests an analogy between surfing ocean waves with a surfboard and surfing cyberspace.
Mathgirl32 is right, Jean Armour Polly is credited with inventing the phrase "surfing the Internet". Read her interview.

Peace always,
<jdenny>