A chain connects the parts in your drivetrain.
All bike chains have a pitch (distance between link pins) of 1/2 inch.
Chains have different widths to work with various shifting systems.
Chain wear happens on the inner chain plates, as they rotate around the pin.
With constructed with bushings, the pin goes through a hollow rivet running through the inner plates, and the roller goes around the bushing (pic). These are an older design but are still used on single speed bikes.
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Bushingless chains have protrusions from the inner plates, which act as a bushing for the roller to go around. They are more flexible, and used on bikes with derailleurs.
Keep your chain clean and lubricated to keep it running smoothly for a long time.
Lube your chain with a drop of chain lube on each roller. Spin the cranks a few times and wipe away the excess. Bushing chains need lube inside the bushing, so put a drop between the side plates instead so it can get under the roller and into the bushing.
You can't tell if a chain has bushings when it is on the bike. You need to take it off and look at the inner plates. You can see the bushing fixed to the inner plates, while bushingless will come apart.
Chains wear as grit between the pins, rollers, and plates grind away material. They "stretch" as these gaps become wider and the link pins gradually get further apart.
A worn chain can wear down gears faster, since the pins are less engaged in the teeth.
A chain will wear more on one side, as the links bend inward and back as they go around the gears. When you remove your chain for cleaning, make sure to replace it in the same direction!
It's best to buy your drivetrain new and keep it running together. Parts with mismatched wear can make some horrible noises.
https://bike.bikegremlin.com/3555/bicycle-drive-chain-dimension-standards/
https://sheldonbrown.com/chains.html
https://sheldonbrown.com/chain-wear.html