Non-custodial ownership means you are in full control of your coins. It refers to the fact that no third party has access to the information necessary to move your Bitcoin on your behalf. An exchange for example, is holding your Bitcoins for you, and in the event that an exchange is compromised, your coins may potentially be unsafe. Non-Custodial is always the preferred method to ensure safety and security on a personal level. (See: Not Your Keys, Not Your Coins)