A wallet doesn't hold coins, it holds keys
Despite the name, a Bitcoin wallet doesn't actually store your bitcoin the way a physical wallet stores cash. Your bitcoin lives permanently on the public ledger as UTXOs. What your wallet stores is a private key, a secret number that proves you have the right to spend the UTXOs associated with it. Lose the private key and you lose the ability to move those coins, even though they're still sitting right there on the public ledger for anyone to see.
From your private key, your wallet mathematically derives a public key, and from that public key, a public address, the string you share with someone to receive payment. This is a one-way street, you can generate a public address from a private key easily, but you cannot work backward from a public address to discover the private key. That asymmetry is what lets you publish your address freely without exposing your spending ability.