You probably don't really have to walk to be a good driver, but it helps. For driving on a track or an autocross course, it helps to know the layout before you drive it, so put on your walking shoes and take a hike. Even the professional drivers in Formula 1 do a track walk before their race weekends, and even if they already know the track, they walk it to look for where to place the car, where to park if they break down, to inspect the road surface, etc. Even in autocross it's a good idea to have an escape plan just in case your brakes fail! I think our teacher taught us this in driver's education class long ago, that driving down a highway you should always be aware of not only what's ON the road, but what is OFF the road in case you are forced off the pavement to avoid an accident. Back in Ohio that usually meant which corn field would you drive into if suddenly the road was blocked, but luckily I never had to do that.
If that walking was too boring, here's my fastest run DRIVING this course:
I've seen various methods of walking the course, so I'd suggest you do it by yourself or with an experienced driver. Most clubs will offer a Novice course walk, and if you're new to autocross this is a great way to hear from the club's expert on how to drive the course. On the video above, I just held the camera in front of me and walked it in an amazingly slow 8 minutes, which turned into about 42 seconds during the event. You'll hear a few conversations of other drivers as they walk past the camera, and since this figure 8 course runs part of the course in both directions, there are people walking both ways all over the place. It might look confusing if all you see are a bunch of cones all over the place, but once you walk it or drive in an autocross event, it's a lot easier.
So what NOT to do on your course walk is to go with a friend and just start talking and telling stories about great pizza or your latest modification to your car. The course walk should enable you to learn the course, and then start figuring out the fastest way to drive it.
Some clubs will provide a map of the course also, so that might be helpful if you're worried about getting lost. We had a map of this course posted on line the day before the event, so that's a little helpful to get the general layout in your head, but it is way more helpful to walk it in person the day of the event. Sometimes I've walked a course and found a spot that wasn't clear which way to go, so if that happens, I just ask someone from the club that knows. Most of the time there will then be some extra pointer cones or chalk marking on the course to clarify. The one exception to there only being one correct way on course is when a slalom of cones in a straight row is "optional", meaning you can start on the left OR the right of the first slalom cone, and then as long as you alternate thru the rest of them you're OK. I like the optional slaloms, because you can look at the entry and exit of the entire sequence and figure out which way is faster. If' it's a toss-up, then drive it both ways in competition and see how it goes!