Running brings me peace - when I run it seems like whatever problem I have just goes away! What does it do for my brain? Well, running gets my brain back to 'right' - it's my time to organize my scattered thoughts; to work out a problem; maybe to play out a difficult conversation in my head (kind of a time to 'prep', if you will). Or sometimes it's even my time to let my brain shut off - just leave all those problems, questions, issues behind and think about nothing more than my breathing, my heartbeat, my footfalls.
So, really, what it all comes down to is this: running is my therapy!