How are gills in a bony fish adapted to their functions?

Breathing

Oxygen dissolved in the water is absorbed by the gills. The movements of the mouth floor and operculum are co-ordinated to produce a stream of water, in through the mouth, over the gills and out of the operculum.
There are usually four gills on each side consisting of a curved bony gill-bar bearing many fine filaments. Through the gill-bar run blood vessels which send branches into the gill filaments. The filaments bear smaller filaments down their length which, in turn, divide into smaller branches. So great a number of minute branches provides a very large surface area when the gills are immersed in water. The walls of the gill filaments are very thin, enabling the oxygen to diffuse rapidly into the blood. A convenient way of visualizing the gills is as an orderly system of blood capillaries exposed to the water in such a way as to absorb oxygen.
The mechanism for pumping water over the gills seems to vary in detail according to the type of fish but, in general, the pressure in the mouth cavity is reduced by the floor of the mouth being lowered. Sometimes the bony operculum is moved outwards as well, assisting the increase in volume. In either case the free edge of the operculum acts as a valve, being pressed against the body wall by the higher outside pressure and so preventing water from entering through the opercular opening.
Thus, water enters through the mouth to equalize the pressure. Next, the volume of the mouth cavity is reduced and the pressure increased by raising the floor of the mouth. A valve inside the mouth, formed by an inturned fold of skin, prevents water from leaving the mouth. The increased pressure forces open the operculum and expels the water through the opercular opening, causing it to pass between the gill filaments as it leaves.
Although there is more oxygen in air than in water, a fish will suffocate in air. This is probably because the muscular system of mouth and operculum which can work in water will not function in air. In other words, the valve system which is water-tight is not air-tight. Another important reason is that when a fish is out of water, the surface tension of the water-film covering the gill filaments sticks them together so that the total surface exposed is very much reduced.