As I seem to recall, the "Surge" was defined at the time (read - this is what the media tended to express it as) as the flow of more combat troops into Iraq. Cav Guy, MikeF, and others have pointed out the more nuanced aspects of it, but most of that didn't make it into mainstream (or more generalized) discussions of it. The "Surge" simply came down to more boots on the ground.

Granted that's a massive oversimplification, but I do tend to think that's how ma and pa back on the couch watching TV saw it (or had it explained to them).