Simmering is the desired cooking method for making stocks because it the stock were to boil, the agitation of the bubbles could disrupt the clarification process, leading to a cloudy stock.
Similarly, proteins are cooked more gently at a simmer as opposed to a boil, which is important because boiled meats will quickly become tough and stringy. This is why sauces, soups and stews with meat in them are simmered rather than boiled. Otherwise the meat would turn out too tough.
With simmering you'll see bubbles forming and gently rising to the surface of the water, but the water is not yet at a full rolling boil.
See Also: Poach, Boil