Boil: reach or cause to reach the temperature at which it bubbles and turns to vapor.
Simmer: stay just below the boiling point while being heated.
Do not mix up boil and simmer. If you boil instead of simmer, you will overcook your food. To simmer food, set the heat to low. To boil food, set the heat to high.
Here are GIFs showing the difference between boil and simmer. Images are from TheKitchn.