A custodian is someone who holds something for you, so a custodial wallet is typically a wallet or exchange who holds your private key, and thus has control of your crypto. If you don’t know your private key, then you’re likely using a custodial wallet.
Custodial wallets simplify crypto by offloading the security to your custodian, however this requires you to trust that the custodian won’t steal your crypto. Custodians are also targets of hacks since they hold lots of crypto on customer’s behalf.
In most cases, you buy crypto from an exchange using fiat money and that crypto is then held in a custodial wallet managed by the exchange. It’s a good practice to then withdraw your crypto from that custodial wallet to a wallet where you control the private key - ideally cold storage.
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