If you know your physiology— or if you've read my book, Modern Training and Physiology—you can probably rattle off a number of reasons. Increased red blood cell count, more mitochondria, deeper capillary beds, et cetera, et cetera. All of this improves your aerobic capabilities, and this is why the first thing to do in order to get faster is to run consistently, and run more.
If you approach the question of why you should go for a run with the mindset of a complete novice, you'll realize there are some obvious points to consider. How far should you run? How fast should you run? Should you run the same speed every day, and the same speed year-round?
"Going running" is the staple starch of a distance runner's training. But I've come to realize that a lot of athletes can't articulate what purpose the plain old boring run serves in training. They know VO2 max, they know lactate threshold, they know marathon pace and critical velocity and hill sprints and creatine phosphate sprints and any number of other highly technical tools of training, but have only a vague inclination of the purpose of just going for a run.
Part of why this question is a little tricky to answer is because the standard run has a number of different uses. This leads to confusion about how fast to run, how far to run, and so on. In order to get a better intuition about the purpose of running generally, and easy running specifically, it will be instructive to look at the range of uses of the "regular run."
Going for a run to improve your aerobic fitness
First, a thought experiment: If a total newcomer to the sport—say, a high school boy who runs 5:30 for the mile in gym class with no running-specific training—starts running 30 minutes at an easy effort every day, will he improve? Certainly, yes. The new stress on his body will stimulate a physiological response in the form of improvements in the "oxygen delivery system"—all those physiological markers of performance that you read about in textbooks.
The same high school runner, a year later, decides to start training harder. He still runs 30 minutes per day, but increases the effort level, running at a moderate to fast pace at least 4-5 times per week. Will he improve? Again, yes. Though the volume of training is the same, the intensity is higher. This, again, creates a new, stronger stimulus on the aerobic system, which responds in turn.
Now consider an alternative: Instead of running faster, our runner decides to run 60 minutes per day, still at the same easy effort as before. Will he improve? Yes. A new and greater stimulus leads to a proportional increase in fitness.
Finally, a third situation: our runner, a year after starting his training program, decides instead to keep doing the same thing—running 30 minutes per day at an easy effort. Will he still improve? Maybe a little bit...but eventually, his aerobic fitness will not get any better. This is one mistake that die-hard Lydiard fans often make—believing that the same training (e.g. 100 miles a week) can produce improvements in aerobic fitness forever.
In reality, of course, high schoolers often do continue to improve year after year with the same training, because they're maturing and developing, which also contributes to performance. And our simplistic thought experiment doesn't take into account the effects of workouts and races. If your workouts are progressing over time, in volume, speed, intensity, or some combination thereof, you can improve your performances even if your off-season training is the same, but that's outside the scope of our topic for today.
So, we might conclude that the purpose of running—in the off-season at least—is to produce a new stimulus on the aerobic system in order to improve our fitness. This is correct, but it's only part of the purpose of the easy (or not-so-easy) run in training.