Now, I got my start as a gamer in board wargaming. Board wargaming, as its name implies, uses a game board with a map on it and, typically, a grid of hexagons. Later I dabbled in miniatures gaming which used a tabletop or space on the floor with a terrain represented but no grid. So when I got into roleplay gaming (lo, these many years ago) I was quite comfortable with using a grid and also with operating on an open tabletop. But battlemats hadn't been invented yet and the closest thing available were blank paper wargaming maps for the do-it-yourself game designers. The problem with those was that they only came with rather small hexes or squares which were too small to properly hold a gaming miniature. Back then a "25mm" miniature was the size of a "20mm" miniature today, although a few makers of historical miniatures had "30mm" lines which were close to today's 28mm figures.
So at the gaming table I fell back on just doing simple sketch maps on the fly with pencil and paper. Several time a session I would say "Okay, quick sketch!" and draw out a very basic representation of the scene. This worked well enough, although with a big table it was often difficult for everyone to see the small sketch well. Later, when some marvelous person invented the erasable battle mat, I bought one immediately--and I still have it.
As a very visually-oriented person I find it absolutely essential, both as a player and as a GM, to have a clear visual representation of what's going on in an action scene. It doesn't have to be fancy--I'm still fine with "Okay, quick sketch!"--but I need to be able to see what's going on. Now I have a friend (Hey, Kaiser!) who steadfastly refuses to give us any visual representation whatsoever of action scenes. It's totally theater of the mind--and it drives me crazy. It's like playing blindfolded. And here's a great example from the http://intwischa.com blog (which I recommend):
GM: The orcs sprint forward, cutting off the wizard from the rest of the party. One lunges in, stabbing Thomas in the shoulder for eight damage.
Thomas' player: Hey, I said last turn that I was backing out of range!
GM: Oh, well, you miscalculated the distance.
Thomas' player: Um, OK. It's my turn then, and I'm going to catch all the orcs in a fireball.
GM: Alright, but you can't get them all.
Thomas' player: You just said all the orcs cut me off from the rest of the party.
GM: Yeah, but they're not grouped together like that
Thomas' player: *sigh* OK.
My games will always have some visual representation for action scenes.