10 Percent

The advice I see everywhere is to only increase the distance you run by 10% each week, especially if returning from injury.

My question: Does this apply the the distance/time for each run OR the total distance you run in a week?

I'd always taken this to mean 10% total distance per week rather than for each individual run.  

So if you did 3x 5 mile runs in one week (i.e. 15 miles total), you could extend one of the runs to 6.5 miles the week after whilst keeping the other two at 5 miles, or you could increase all three runs to 5.5 miles 

Yes, I'm pretty sure it's distance.  Increase it by 10% in total each week, but take a rest week every third or fourth week where you run a lot less miles.  Then the following week, just add on 10% of your previous highest.

The 10% rule is one of those things of which nobody has yet pointed me to the source.  It arises out of experience as far as I understand, and is not tightly formulated.  Personally I apply it to each run, which has the benefit of ensuring that I don't go over the 10% each week.  Therefore I would never be able to do what stutyr suggests.  I don't think the example is actually bad, but at more extreme positions than 15 mpw, it would need to be tempered.  If you were up at 80mpw, progressing towards 100mpw, adding 8 miles onto one run might be counterproductive and stressful.  Like I say, it would be tempered - you wouldn't actually consider doing that.

I also know from my own experience that adding just one mile onto a long run (over ten miles) can be fatiguing and stressful.  In previous marathon training I've got up to 15 miles and then started adding half miles just to be sure I'm not overdoing it.  One mile would probably be (and has been) fine.  Moving straight up to 16.5 has felt like a step too far!

Whilst you're starting experimenting with what works for you, 10% is a good guideline to bear in mind.  Sure, I think if you're regularly running, short to middle distances, you can add more than 10% per run safely if you stick within the 10% per week.  As you go longer you'll see what works for you.