When we put bits into the mouths of horses to make them obey us, we can turn the whole animal. Or take ships as an example. Although they are so large and are driven by strong winds, they are steered by a very small rudder wherever the pilot wants to go.
Don't get this verse confused by the previous verse. In the previous verse it says that the person who can control his tongue can keep his whole body in check. This is not to say that the tongue is like a bit to your body. These verses will be explained in the next verse. They are simply building a mental picture of how something small can affect something big.
A bit is small, a horse is big. A rudder is small, comparatively, to the big ship. Small things can sometimes impact big things. We are going to see that the tongue is like that.