A cogwheel is a wheel mounted on an axle used in gear systems, which has cogs (sometimes called teeth) on the circumference which interlock with cogs of other cogwheels.
There are two important parameters of cogwheels. One is the size and shape of the cogs. If one cogwheel is to turn another, the cogs must be compatible (e.g. one cogwheel with teeth 20mm apart will not be able to turn a cogwheel with teeth 8mm apart). The cogs in precision systems are machined carefully so that there are always at least two points of contact between two wheels. (The shape of these cogs is not simple - it takes some clever geometry to make cogs with that property.) This ensures there is no 'slack', that the gears are never loose and never rattle - if one wheel is motionless, the second cannot move either. The second parameter is the number of cogs on the wheel (which means, given that the size of the cogs is predetermined, the size of the wheel). If a cogwheel with 40 cogs turns another with only 20, the second axle will make two revolutions for every one the first makes.
One significant variation on the design is the directed cogwheel. If two axles are connected by a spring, pulling them together, and a latch is properly positioned, the cogs can be designed so that if the 'drive' cogwheel rotates one way the second wheel will turn too becuase the cogs catch each other, but if the drive rotates the other way the second wheel will not turn (at least, not more than the angle between the cogs) because the cogs slip over each other. Friction can wear down directed cogs, but for some applications they are useful - e.g. in a grandfather clock, the to-and-fro swinging of the pendulum can be converted into motion which is only clockwise. Slightly jerky motion, but the irregularity is so miniscule that when it gets to the minute hand it is unnoticable. (Most designs involving directed cogwheels are not as crude as this - axles do not usually move, except for rotation. There is a clever component called an escapement which relies on a spring (or weights) to pull a wheel in one direction, which performs the same function with rigid axles that don't have to move relative to each other.)