1) the physical act of, basically, moving your feet in a fast rythmic motion to propel yourself forward at a greater speed than if you were walking or jogging.
2) a sport, wherein people run as a form of athletic activity as opposed to merely another action that a person can take. In other words, they run for the sake of running (or in order to compete with other individuals in an event called a "race
.") Some people totally dedicate themselves to this sport, to the point where it is a major part of their lives. Others do it on a fairly regular basis in order to stay in shape, or as part of a training/workout regimen.
Still others run occasionally, when they feel like it.
In order to run well, it helps to have good form (running incorrectly can put stress on your joints and be even more painful), good endurance, patience, and commitment (you don't just give up after 5 seconds, or you'll never get anywhere).
1) He was running through the snow to escape the grizzly bear. Then, he realized this was rather stupid because trying to outrun a grizzly is pretty much pointless. They're too fast.
2) The cross country kids went running after school. Everyone else stared at them funny because it was 25 degrees out and snowing.