When you keep assets on a centralized exchange, the exchange holds the keys. You see a balance in your account, but on-chain those funds sit in wallets the company controls.
Self-custody means you hold the keys yourself — in a software, hardware, or smart wallet. You gain sovereignty and portability, but you also accept full responsibility for backups and security.
The phrase "not your keys, not your coins" captures the tradeoff precisely. Custodial services optimize for convenience; self-custody optimizes for control.