A custodial wallet is usually an online service.
With custodial wallets, private keys are held by a third party, e.g. a crypto exchange or a wallet provider, which means users don't really control their crypto assets. Instead, users have to trust that the third-party custodian will secure their crypto for them.
Find out more about crypto-exchanges
A non-custodial wallet (also known as self-custodial), on the other hand, gives users full control over their private key, and with it sole responsibility for protecting their holdings.
What is the difference between Hot vs Cold Wallets?