Ossicles in general are very small bones. When people use this word, they are usually referring to the auditory ossicles, the smallest bones of the body. All mammals have ossicles which make up an important part of the system which allows them to hear. Absence of the ossicles will not necessarily result in deafness, but it can cause hearing impairment. Likewise, damage to the bones acquired later in life can also damage the sense of hearing.
There are three ossicles, known formally as the incus, malleus, and stapes. People often refer to these bones with their common names, the anvil, hammer, and stirrup. The names reflect the shapes of the these bones. For perspective, the ossicles found in the human ear are generally small enough to fit comfortably inside one of the number keys on your keyboard, although they can vary slightly in size between individuals.
The system through which these bones work is rather ingenious. When sound enters the ear and vibrates the eardrum, the movement vibrates the malleus, which is attached to the eardrum. The malleus in turn vibrates the incus and then the stapes, which transmits the vibrations into the inner ear. The ossicles act to amplify the vibration to make it stronger, allowing people to discern sounds better than they could without these bones in place. While it is possible for sound to travel from the ear drum to the inner ear without the ossicles, it will be weaker and harder for the ear to interpret.
However, the ossicles are not designed to vibrate completely at will. They are controlled with muscles which can limit the vibration of the bones if a sound is too loud. Extremely loud noises have the potential to damage the ear if the ossicles are allowed to vibrate freely. The muscle control ensures that they will not vibrate too much. Even with this protection, it is possible for the hearing to be impaired with loud noises, which cause pressure waves that can interfere with hearing. Likewise, pressure waves caused by explosions and other events can also hurt the ears.
These bones can be damaged by severe infections and cancers which penetrate the middle ear. There have also been cases in which people have had hearing damage as a result of blows to the ear or head which damage the interconnected systems of the ear. Such damage can result in a temporary ringing sensation which resolves eventually, or long term damage caused by serious injuries.