I was going to post the same paper as Brazillian Guy, it's nice to see someone going to the same well for ideas.
For a minute I want to take a step back from Does mileage do this? Does mileage cause that? This is one of those topics that's almost become political in running. Are you Quality or Quantity? Just about everyone has an opinion and for most of us it's the thing we did as runners that we lean toward. I was definitly in the quality camp, but since becoming a coach I've had successful athletes running around 90-105 miles a week and successful athletes under 30. By now I don't think I have much a horse in the race on that debate.
Runners improve when we are challenged. Runners get injured when we are too heavily challenged. Runners stop improving when we aren't challenged enough.
Mileage is no different. A kid with reasonable talent in high school can run 40 miles a week and be pretty damn good. But it doesn't make sense to then say, "let's stay at 40 miles a week in college and when he goes pro or if he moves up to the marathon." Spending years and years at 40 miles a week doesn't make sense from a development standpoint. After some amount of time that kid will be used to it. 40 won't challenge him or her. Runners improve when we are challenged.
That doesn't necessitate a climb up to 80 miles a week. Hell, 45 miles might be plenty for him to adapt to as a next step. Capillary beds expand, the heart increases in size, mitochondria are a little more strained and increase in density. That small jump can also add some fatigue going into each workout, that's another thing to adapt to.
We need to stop the vilification of higher or lower mileage. Add a variety of challenges to an athlete over enough time for them to not be overwhelmed and you'll get a pretty decent runner; at least a better one than you had before.
Getting back to the thread: How does mileage improve performance? Mileage is our surrogate for volume. When we run more, our bodies adapt so that the stress that we cause it can be met with appropriate fitness to handle it. Mileage (in this case aerobic running) causes adaptations of the muscle (improved strength, mitochondria, glycogen storage, coordination), heart (increase in size/stroke volume), blood vessels (increase the density and number of capillary beds to deliver blood/oxygen and remove waste from muscle), and blood itself (improved oxygen transport and enzymes for aerobic respiration). Not to say that's an exhaustive list.
At the end of the day, the upper echelon of our sport can be a war of attrition. Sometimes the reason a Pro "makes it" is because they were one of the guys/girls out there that had some talent but also had the ability to run a lot. It's hard to beat someone who runs twice as much as you it they're also pretty talented.
You can find people running relatively little. You can find people that run a whole lot. But don't take anyone too seriously who says it has to be one way or the other. Every runner is different, but every runner needs to be challenged to get better.