The most common type of gearbox is a standard spur gear configuration. These are the simplest gearbox to make and so is the most common and cheapest to manufacture. Spur gears are straight cut gears intermeshed together to form the gearbox. They have straight teeth that mesh with other spur gears to reduce speed and increase torque or increase speed and decrease torque or change rotational direction. Generally it takes many spur gears to make large reductions and space is always a limiting factor when designing these.
While spur gears and common and cheap to buy, they aren't always the best solution, especially where high torque or speed is required. They can be quite noisy to operate and the stress on the gears can be destructive if too much force is applied.
Below, picture of a Spur gear set. If you were to drive the large spur gear, the smaller one would revolve much faster meaning that there would be a torque reduction and a speed increase on the other spur gear. If you ran the smaller spur gear there would be less speed transferring to the bigger spur gear but the torque would be greater.