What is a store credit?

Probably, credit extended by a store to its customer.

It's not "a" store credit. It's just "store credit". It basically means having an account with a store, or shop, so that you can have goods now and pay for them later. Most shops that offer this facility issue a "store card". It's a bit like a credit card except it is only valid for one particular store or store chain.

If you return something to a store (like a sweater that doesn't fit), some stores won't give you money back (especially if you don't have a receipt). Instead, they let you buy something else.

Basically, it's like having money in that particular store (but can't spend anywhere else).