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Charles-Tim explained, a paper wallet is basically your private key written on some physical medium, like paper or engraved on a metal plate. Nowadays, a similar method is often used, but not with private keys, but with backup seed phrases from which countless private keys and associated addresses can be derived.
However, a "paper wallet" is not a substitute for a hardware wallet, because a hardware wallet allows you easy access to your wallet and coins, so it is more convenient. A paper wallet (if created in a secure way) is good only for long-term hodl.