About Private Key
MetaMask is a wallet "management tool". The real "wallet" is a pair of wallet address, it consists of public key and the private key.
Public Key = Receipt Number. Can be disclosed publicly to receive fund.
Private key = Wallet key. Anyone with a private key can access the wallet.
So if you have back up your private key, you can resume your wallet operation in any wallet "management tool".
About Seed Phrase
If you have a 12-word seed phrase, MetaMask or any e-wallet that supports ERC-20 system can generate an unlimited set of e-wallet address based on your seed phrase. So backing up seed phase is equivalent to backing up your wallet (public key and private key).
The consequences of losing the private key and seed phrase
The private key and seed phrase are the only way to recover your e-wallet. If you lost both of them, you will never be able to recover the wallet again. Same as losing your wallet on the street. Therefore, be sure to back up and keep your private key and seed phrase in a safe place.