Nick B has got it pretty much right.
Basically, as it improves it lets you run at a faster pace more comfortably.
Horwill states it as.."It is a measure of fitness, and literally means the amount of oxygen we can breathe in during one minute of maximal work and is expressed as millimetres per kilogramme per minute."
http://www.serpentine.org.uk/advice/coach/fh49.php- explains about it well.
It is one of the key elements of running well. The other 3 are...endurance ( covering the distance), basic speed (how fast you can run flat out) and lactate threshold.
ASsuming you can cover the 10k distance comfortably ( which if you can't getting to 50 miles a week ENSURES you can and so can bring massive performance gains), then vo2 max and lactate threshold are more or less equally important.
vo2 max is about just how fast a pace you can run, your lactate threshold is the percentage of your vo2 max ( or pace), that you can keep up with without lactate starting to gather in the legs, if you're running above your lactate threshold, it accumulates and that's why you start to slow down.
For instance if you have two runners, both of whom have a vo2 max at say 6mm, the one who has a higher lactate threshold SHOULD win, say one has 70% the other 80%.
But unless you have a programme aimed at improving this, running 50 miles a week gives you substantial vo2 max gains, odds are as long as you do some bits faster you'll naturally improve your lactate threshold and your base endurance will increase substantially.
THis is all stuff you don't really need to know, but the truth is that just about every runner I've known has seen SUBSTANTIAL performance gains from moving up to 50 miles a week (slowly and progressively). I know that my own performance went from around 45 minutes to around 38. (debut was 61 minutes, now running 33 minutes, expecting a sub 32 clocking within a year, probably would have had already but have had injury for last 4-5 months, but managed to sustain some sort of performance so still just at sub 34 standard).