An internal combustion engine needs a transmission for two reasons. An engine is not powerful enough to push the weight of a car down the road and an engine does not have the RPM range to drive at all necessary speeds with only one gear. If you feel like experimenting, next time you are driving a car with a manual transmission, try starting off and driving only in 3rd gear. It will be difficult to get moving but not impossible, you will have almost no acceleration until the engine gets into its power-band and the engine will absolutely scream for mercy at highway speeds. Fuel economy would also be terrible. So we need gear reduction so the engine can have a mechanical advantage over the wheels to get the vehicle moving and direct drive or even a slight overdrive for highway cruising, and we need a device to change gears. Gears can do two things. They can increase torque and decrease RPM (underdrive), or they can decrease torque and increase RPM (overdrive).
Underdrive (Gear Reduction)
A typical first gear has a gear ratio of 2.6:1. That means that for every 2.6 revolutions of the engine/input shaft, the output shaft turns once. This does two things, RPM is divided by 2.6 and torque is multiplied by 2.6. So an engine that has 200ft/lb (271Nm) of torque at the crankshaft, has 520ft/lb (705Nm) of torque at the transmission output shaft in first gear. However, if the engine is spinning at 2000RPM then the transmission output shaft is only spinning at 769RPM. In most transmissions, all gears except the top gear is an underdrive gear. The final drive also provides further gear reduction.
A typical top gear ratio has a gear ratio of 0.4:1. That means that for the engine/input shaft to turn the output shaft once, the engine only needs to turn 0.4 times. Once again, this means that RPM is divided by 0.4 and torque is multiplied by 0.4, So and engine that has 200ft/lb (271Nm) of torque at the crankshaft, has 80ft/lb (108Nm) at the transmission output shaft in first gear. However, if the engine is spinning at 2000RPM then the transmission output shaft is spinning at 5000RPM. In most 3-5 speed transmissions, only the top gear is an overdrive gear, but even in overdrive the wheels do not spin as fast as the engine because of the gear reduction in the final drive.
A direct drive is a gear ratio of 1:1. That means that there is no change in torque or RPM through the transmission. This is a typical 3rd gear.
Helical Cut Gears
The teeth of most transmission gears are helical cut, meaning the teeth are cut on an angle. This allows multiple teeth to mesh at the same time on the same gear. This makes for a stronger connection as well as quiet operation. Many cars with manual transmissions have straight cut reverse gears, you may notice a whining noise in reverse that gets worse with age/use.