I started running in high school out of pure compulsion. I always hated running but I got to a point that I felt compelled to just go. I found it a good emotional regulator (especially with the right soundtrack) and found it changed my mental state and I felt better after each run.
In college, I challenged myself to run a half and then a full marathon. I ran my first 2 in Tucson (not on an official race).
The first time I attempted it, I actually failed.
But I learned from that and used it as a stepping stone to successfully running my first 26.2 miles.
It changed my life. 
It shattered my limiting belief of what I was capable of and what was possible. I believe  everyone should run a marathon (and skydive) at least once in their lives if they can (or even if they can't) because it's a magical experience.
Running has positively impacted my life in many ways. 
Socially, mentally, physically, emotionally, and I'd go as far as to say spiritually too. It's a great teacher.
Running is a reminder that if you don't stop you can get to a place you want to be at no matter how far it may seem. It's a reminder to keep going, to breathe, to question what you're capable of and to attempt pushing yourself past that perceived limitation.