Simply put, your VO2 Max is the measure of how much oxygen your muscles are able to use. No one is able to utilize all of the oxygen in their bloodstream. But, the more you are able to use, the faster you'll be able to run.
In order to increase your VO2 Max, you don't actually need to know what yours is. -- which is good since measuring it often involves a lot of lab equipment and a really painful testing protocol. What you do need, however, is an idea of your velocity at VO2 Max -- (v)VO2. For most people, (v)VO2 is going to be roughly the pace you can hold for 10 minutes of all-out running...
Measuring your (v)VO2 Max
Instead, we substitute 1k repeats and shorten the rest to 2 minutes. 1k is still long enough to stimulate development, but beats them up less and allows them to have a stronger workout in the following days. But, really, any distance you enjoy will work -- or a ladder workout that mixes the distances (800, 1k, 1600, etc.).
In addition to these basic VO2 Max workouts, there are other, more race specific ways to get the same result -- especially if you're training for something other than the 3k/5k. I'll talk about those in a later post, but remember these simple guidelines and you'll be bumping up your VO2 Max in no time!