The rest of what follows explains RICE and what you need to do. When you are injured, fluid accumulates in the injured area causing swelling. Swelling limits motion of the injured area and may contribute to paint if it is severe enough. RICE is important because swelling is hard to reverse once it's been there awhile. You want to prevent it in the first place.
Rest is necessary to keep an injury from getting worse.
This doesn't mean you have to totally stop. You can try continuing an activity if pain allows. If the pain persists stop the activity. Ice can effectively decrease pain from an injury. Icing deadens pain and increases blood circulation to the skin which is OK and decreases circulation to deeper areas where bleeding may be occurring.