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Ethereum wallets are applications that let you interact with your Ethereum account. Think of it like an internet banking app – without the bank. Your wallet lets you read your balance, send transactions and connect to applications.
Your wallet is only a tool for managing your Ethereum account. That means you can swap wallet providers at any time. Many wallets also let you manage several Ethereum accounts from one application.
That's because wallets don't have custody of your funds, you do. They're just a tool for managing what's really yours.
Read more about wallets at Ethereum.org