Wheels do not exist in nature, and no animals use them except people. Even people didn’t use wheels until the early Bronze Age, around 3500 BC, much later than the other simple machines (the lever and the inclined plane).
The earliest evidence for people using wheels comes from Sumeria (modern Iraq), about 4000 BC, just about the time when people first began to live in cities. The earliest wheels were probably not wagon wheels, but pottery wheels. Soon after that, though, maybe around 3700 BC, people in Central Asia were making wagon wheels. Spokes developed later than solid wheels.
Wheels help people do work in two ways. First, like levers or inclined planes, wheels allow you to do something easy for a longer time, instead of doing something hard for a shorter time. If you turn a large wheel fixed to an axle, the axle will also turn. You can turn the large wheel easily (but it takes a lot of turning to go all the way around). The axle will go around a much shorter distance, but with more force.
So you can use a wheel to create a mechanical advantage – you can turn something heavy, by spinning a large wheel attached to an axle that is attached to the heavy thing. That’s how a pencil sharpener works. Or, you can do it the other way around – use a lot of force to turn the axle, and that will spin the wheels really fast. That’s what cars do. You get more mechanical advantage with bigger wheels and thinner axles – the mechanical advantage of a wheel and axle is the ratio of the radius of the wheel to the radius of the axle – but bigger wheels and thinner axles are also more likely to break, so you have to find the best proportion for your specific use.
Also, wheels on a wagon only touch the ground at one spot at a time, keeping the rest of the wagon off the ground. This makes less friction, so that the wagon is easier to move than if you were pulling it along like a sled.
A gear is a special kind of wheel with teeth that fit into the teeth of another wheel (so a gear is also a kind of lever, because wheels are a kind of lever). Some kinds of grasshoppers have evolved to have legs with gears in the joints to jump with. Whoever invented gears, the idea spread quickly: Indians were using gears for waterwheels by the 300s BC. Greeks knew about gears by the time of Aristotle, about the same time, and people were also using gears in China. By the early Middle Ages, people all across Afro-Eurasia were using gears to run watermills and windmills.