Non-custodial means that a third party does not have ownership of your assets in a service.
A non-custodial model usually means s smart contract based service model where the owner of the assets never lose the control of the assets. This is opposite to most traditional finance services where you cannot see what happens to your money after the deposit or whether you are able to withdraw. The integrity of the service provider in the traditional finance thus needs to be guaranteed through regulation or government bailouts. The non-custodial model is specific to smart contracts and cannot be achieved without a blockchain. Read more.
Non-custodial protocol models have become popular in a blockchain, after FTX and Celsius blow-ups: not your keys, not your coins.
See also
Wallet
Custodial
Decentralised finance
Protocol