In a nutshell, repetitive, strenuous exercise such as running creates micro-tears in muscle tissue. As the tissue heals, it can shorten, causing tightness and shortening range of movement. By stretching afterwards, you are trying to prevent tightening occurring. Bear in mind that many runners stretch at home whilst watching TV and the like - the key is to do it gently. You can stretch from cold without worry, as long as you don't follow it with exercise and do it very gently. Over time you'll improve flexibility, which can potentially decrease injury risk.
NEVER stretch from cold before exercise. I got a lecture from a physio on this. Not only will the subsequent exercise potentially tear the muscle, but it can tear the neural tissue which connects the muscle. NOT recommended.
The best warm up is to enact the exact activity you intend to carry out, but at a far reduced level of exertion, e.g. 5-10 mins brisk walk, 5-10 mins jog - 5-10 mins slow run, go fast intervals!
edit - I should say that warming up / down is a highly contentious debate. Many will argue with what I've written above, so maybe the best plan is to take what makes sense to you from every side and go with what works for you.
Edited: 10/01/2011 at 00:40