A non-custodial solution, also known as a self-custodial solution describes any method of storing bitcoin which does not give a third party access to a user’s private keys. A user who self-custodies their bitcoin cannot have their transactions censored by anyone. The risk of confiscation, either by the custodian or the local government, and the loss of privacy associated with custodial solutions are both avoided.
However, with control over private keys comes responsibility. If you self-custody your bitcoin, no one can be blamed if you lose access to your private keys. Storing multiple copies, dividing your bitcoin holdings between wallets, or using multisig can fortify your self-custodial solution.