Your wallet is like your Ethereum account. You use it to connect to the Uniswap app and other decentralized applications (dapps). This is similar to signing in with Google, except you are signing in with your own Ethereum address that is saved in your wallet.
To start using the Uniswap app, connect your wallet by following these steps.
Visit https://app.uniswap.org/ and click 'Connect Wallet'
Select your wallet from the list. If you don't see your wallet in the list, select 'WalletConnect' to get a QR code that your wallet can scan.
Your wallet will prompt you to confirm this connection, either in your browser or on your mobile device. Once you confirm, you'll be connected to the Uniswap app and ready to trade!
When you trade, you are sending and receiving tokens to and from that wallet. This is a key attribute of all decentralized apps: you hold your tokens in your wallet and authorize transactions with your private key. In contrast, centralized services like Coinbase take custody of your assets and authorize transactions on your behalf after you've signed in with password.
Your wallet is the gateway to decentralized applications.