I hear it's better to stretch after you exercise then beforehand. Why is this so?

While your question seems simple, the topic of whether to stretch before or after exercise is actually quite complex. If by “stretch” you mean a static stretch where you hold a position for several seconds, then it seems to be favorable to practice this type of general flexibility training for the whole body after a workout. Post-exercise static stretching is beneficial because the soft tissues are warm, which reduces the risk for injury compared to stretching a “cold” muscle. Plus static stretching combined with deep breathing can be a great way to add relaxation to the end of your workout. Also, there is some evidence that stretching a muscle for longer than 60 seconds before intense exercise can dampen the muscle’s ability to produce force, so saving it until the end makes the most sense.

The issue of stretching before or after a workout is made more complex when you take into account the different types of mobility work that also fall under the stretching category. For example, self-myofascial release using a foam roller is a form of stretching that is often recommended prior to exercise, along with focused static stretching, for muscles that need special care due to improper movement patterning. For application of these types of mobility techniques, your best bet is to consult with a fitness professional who has specific training in this area.

Source: http://www.acefitness.org/article/3068/