A custodial wallet is a Bitcoin wallet where a third party (usually an exchange) controls your private keys. This means that the provider stores your Bitcoin for you.
Examples of custodial wallets:
Exchange wallets on trading platforms
Online wallets from crypto service providers
Some software wallets for Bitcoin (such as Wallet of Satoshi)
The opposite is a self-hosted wallet, such as the Coinfinity in-app wallet. With this, you control the private keys yourself and have full control over your Bitcoin.
The most important difference: With a custodial wallet, you trust a third party. With a self-hosted wallet, you have full control.
Don't forget: Not your keys, not your coins! 🔑