In a custodial wallet the private keys are held by the service provider: an exchange, a payment intermediary or the casino itself. You see a balance and can issue instructions, but somebody else signs the transaction. The opposite is a non-custodial wallet, where the keys are yours alone.
The practical difference
Your balance is a claim against the provider, not an asset held in your name on a blockchain. If the provider freezes the account, the money is frozen. If the provider disappears, the money goes with it.
In return you get convenience. A password can be reset, support answers, and losing a seed phrase does not mean losing everything. Managing your own keys is a freedom that comes with total responsibility.
The casino context
A casino balance is always custodial — which is precisely why you should not delay withdrawing. Money in a casino account is the casino's promise. Money in your wallet is yours.
An exchange account is custodial too. It is convenient for receiving a payout, but an incoming payment from a gambling site may trigger a review.
Rule of thumb: a custodial wallet is good for passing through, not for holding. Larger sums belong somewhere whose keys you control.