Equilibrium refers to a state in which all of the external forces on an object all balance each other such that there is no net effect (net force equals 0). An object in equilibrium will not experience acceleration, and will either remain at rest, or continue moving at a constant velocity. Here's a simple example, pick up a book (or any random object) and hold it up in the air. The book is now in equilibrium, the downwards force of gravity is perfectly countered by the upwards force that you are applying to it. Notice that the object neither falls nor goes upwards (i.e. no acceleration). Now let go of the book, notice how it falls downwards till it hits the ground (or whatever was beneath it). That is because without the upwards force applied by your hand, the object is no longer in equilibrium, and the force of gravity takes over until it is in equilibrium again.
It could prevent the key from sinking because the wood would float.
It floats because it weighs less than amount of water it would have to push out of the glass if it sank. Wood, cork, and ice are all less dense than water, and they float; rocks are more dense, so they sink. A key would also be more dense causing it to sink.
