A digital/crypto wallet will store your private key. With this private key, you can access your cryptocurrencies and use them however you want (purchase, sell, transactions).
You can imagine that a digital wallet works similarly as your bank account. The wallet does not physically store your cryptocurrencies, but instead, it protects the access to your cryptocurrency.
It is very important to reiterate that a crypto wallet doesn’t store your coins. It stores the private keys required to spend those coins. The coins, which are in the form of unspent transaction output, exist only on the blockchain.
For a more detailed explanation on digital wallets, please see our article: Useful info on digital wallets.