Although it’s not anything like the valves we use to turn on the water at the sink, car engine valves have basically the same role. They are mechanical devices responsible for enabling or preventing fluid flow. This, particularly wise conclusion, hides the fact that the valves of an automobile engine must pass gases, and another fact is that they must be able to do so very quickly.
If we take into account that with a four-stroke engine in one work cycle (during 4 strokes) each valve opens once, and the crankshaft turns twice, it is easy to calculate that each valve will open at an engine speed of e.g. 6500 rpm open and close 3250 times per minute.
The theory says that in a four-stroke engine, the mixture of fuel and air is sucked into the cylinder at the moment the intake stroke begins, that is, when the piston starts to move from top dead center (GMT) to bottom dead center (DMT). Also, we can assume that for a perfectly proper operation of the engine, it is possible to open the intake valve a moment after the piston has moved down so that the created negative pressure helps to suck the mixture.
Equally, we could start closing this valve when the piston has traveled about 80% of the way down because after that the created negative pressure (which sucks in the mixture) will become almost unusable. But this whole theory falls apart as the engine revs increase.
Namely, at higher operating speeds, less time remains for suction of the mixture, and such a (theoretical) engine would suddenly lose power. Adequate to the intake theory, we can also talk about the exhaust valve. It would be ideal to open it when the piston starts to go towards GMT (from bottom dead center), i.e. with the start of the exhaust stroke. However, the problem of speed arises again, because at higher engine revolutions, time may soon run out to “drive” all the exhaust gases out of the cylinder.
Let’s also say that the mixture of fuel and air (for atmospheric engines) is introduced into the cylinder exclusively by the negative pressure created by the piston in its movement towards the DMT. The exhaust gases are then ejected by the pressure created by the piston moving towards the GMT. That pressure is much more efficient in moving gases than the mentioned negative pressure (it would be silly to say that the pressure is stronger than the negative pressure, right?) and therefore the intake valves are usually larger (larger in diameter) than the exhaust valves.