Why would you run as a cyclist? There are lots of reasons, such as social (your significant other or friends are doing it), you just feel like it, or to help you with cycling.
Running can be of use to cyclists in two main ways: 1. make your bones stronger 2. get faster for specific disciplines.
RUNNING FOR TIME TRIALS
Running is an excellent way to work out your aerobic system at a high heart rate level, in a way that is difficult to do on the bike unless you're on the trainer. That said, the better place to do this is on the trainer so that you can condition the specific muscles as well as get comfortable in the TT position.
RUNNING FOR CYCLOCROSS
In a CX race your heart rate is usually at the limit the entire time, and the naturally high heart rate you get while running works well for that. Also, as someone who can run pretty okay, running past other cyclists on the runups is an excellent way to gain some time.
RUNNING FOR YOUR BONES
If you do nothing other than riding, and you do only that for a long time, you will become weaker at everything other than cycling. The impact of running helps your body continue to rebuild and work on your bones.
THE NEGATIVES OF RUNNING
I've heard, and believe, that the pounding of running bangs up and shakes up a cyclists muscles in a way that deteriorates the muscles. For bike racing, which rewards top end speed on top of good base aerobic fitness, running only helps the base part of your fitness. I think that running is a fine thing to do in the CX or offseason, but should be avoided during the race season.
(photo courtesy of the excellent, though for long not updated, blog: https://andrewcycle.wordpress.com)