Because "sprocket" is the name decided on for a toothed wheel that hooks up to a chain, and that's how most bicycles are powered.
Due to the fact that there's more than one on a bike, people have also had to come up with other names to be able to tell them apart.
Adult bikes have chainwheel(s) up by the pedals and sprockets (or maybe a cassette, made up of several sprockets) by the rear wheel.
A BMX, confusing enough, can have the sprocket by the pedals, and a driver by the rear wheel.
In order to create a gear ratio you have to have different sized sprockets.
It depends on whether you are talking about the front sprocket (the one at the pedals, called a chainring) or the sprocket at the rear derailleur. The lowest gear at the front is the smallest sprocket/chainring. The lowest gear at the rear is the largest sprocket. So if you combine the smallest sprocket at the front with the largest sprocket in the rear you have the lowest gear available on your bike.
Chain is on the smallest sprocket on the crank and on the largest sprocket on the rear wheel
25/9 gear ratio
Even slower
In the drive train you have the front chainwheel/ring and the rear sprocket that both engage the chain. The pointy bits on sprocket and chainwheel which allows the chain to grip are called teeth. The ratio between the tooth counts is what determines which gear ratio the bike has.
On a bike there's one(or more) front sprocket(s) by the pedals connected by a chain to one(or more) rear sprocket(s) by the rear wheel. As the wheel isn't driven directly by the pedals, and there's usually a difference in size between the front & rear sprocket this constitutes a gear.
the smallest sprocket is the highest gear.
First gear on a bicycle with external/derailer gears is with the chain on the smallest chainwheel(by the pedals) and the biggest sprocket(by the rear wheel).
If its a road bike, chances are its geared exactly correctly to match power with top speed. Essentially if you add teeth to the rear wheel sprocket, you will shorten the gearing and the engine will hit top revs in top gear before the bike reaches top speed. If you add teeth to the engine sprocket, the opposite effect, less torque in top gear leaving the bike short on top speed.
The sprocket on the nose of the crankshaft that drives the cam sprocket.
A bore kit does not make a bike faster. It makes the engine more powerful if you want to go faster you must work on gear ratios and or sprocket sizes.
Because for most types of riding you want the rear wheel to turn faster than the pedals, and that is achieved by running the chain over a larger sprocket at the front and a smaller sprocket at the rear. By having this difference in gear ratio you get a useful travelling speed at a comfortable pedalling pace (and strain).