Centralized exchanges (often shortened to CEXs) can be a convenient place to buy cryptocurrencies and tokens. However, once you purchase your assets, they are often held in a custodial wallet on the exchange. This means that the exchange itself holds the private key for that wallet address, and therefore has ultimate control over those assets.
If you want to participate more actively in web3, or just want to move your funds for security or peace of mind, you'll need to move the funds off the exchange. A self-custodial wallet like MetaMask can be more suitable for these purposes, since you need a self-custodial wallet to manage your digital identity properly. Self-custody means you hold the wallet's private key, and that you are solely responsible for controlling the assets in your wallet.
To move your funds from a CEX to MetaMask, follow these steps:
A note on wallets
For simplicity, we normally refer to crypto wallets 'holding' assets. This isn't strictly true: the blockchain is the place which records changes to wallet balances. All your wallet is for is verifying that you are the owner of the address, and that you have the authority to move those funds around. So when we say there are funds in your wallet, what we mean to say is that your wallet address has some attributable to it, as recorded by on-chain transactions.