The clutch mechanism in your hub is sticking. if it's a bike with external gears try pulling the wheel from the frame, laying it with the sprocket side up and then shoot some WD-40 or similar thin oil into the hub, see if that will free something up. If that doesn't help take it to a bike shop.
a bike chain basically does two things: it transmits power from where the rider can easily deliver it to the rear Wheel it creates a gearing ratio between how fast the pedals turn and how fast the rear wheel turns. If wheel and pedals turn at the same speed, the overall speed for the bike becomes quite limited.
To transfer power from the pedals to where it can be used - the rear wheel.
It allows the chain to transfer power from the pedals to the rear (drive) wheel.
Penny Farthings didn't use chains, they were direct-drive, with the pedals bolted to the front Wheel axle.
because of the gear ratio and the chain
Wheel Seat Handlebars Chain Pedals
Because it's an easy way to transfer power from the pedals to the rear wheel, and to arrange for a gearing ratio as well.
Putting weight on the forward pedals puts tension on the chain, which rotates the rear wheel and pushes the bike forward.
Pushing on the cranks puts tension on the chain, which rotates the rear wheel and pushes the bike forward.
The diameter, together with the gearing ratio between the chain ring by the pedals and the sprocket at the rear wheel is what decides how far the bike will travel for each full turn of the pedals. If you keep the gearing ratio the same, but switch to a bigger wheel the bike can go farther - but pushing the pedals will become harder. If you keep the gearing ratio the same but switch to a smaller wheel the bike will go shorter, but pushing the pedals will get easier.
Just fine, thank you for asking. The chain transfer power from where it's generated by the pedals to the rear wheel where it can push the bike forward. The gears on a bike work just like any other set of gears, they allow you to trade power for travel - or the other way around. If spinning the pedals is too easy and you can't crank them round any faster, then a change of gears will make the rear wheel turn more WRT the pedals than before, bringing more resistance to the pedals and more speed to the bike. If turning the pedals is too heavy, then dropping a gear will make the pedals easier to turn on the cost of the rear wheel spinning a bit less for each turn of the pedals
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).