Digital wallets are very different compared to your physical wallet. What does a cryptocurrency wallet do? It stores your private and public keys, enabling you to send and receive coins through the blockchain. It also monitors the balance of your cryptocurrencies.
What is a private key? Private keys are like a pin number which you use to access your money in your bank account. When you use your wallet to do a transaction, you send a value, which transfers the ownership of your coin to the recipient.
What is a public address? Every user who has a Bitcoin or cryptocurrencies receives a public key which matches the private key of his public address. When a coin is being transferred from your wallet to the public address it goes into that person's wallet. It is secure and lives on the blockchain.
Ownership of your private keys gives you total control over the funds associated with your corresponding public keys. It is vital to make sure you keep your private keys secretly hidden so that only you know your private key. You can lose all your funds if you lose your private key which makes it imperative to have a backup.
You can write it down on a piece of paper and put it in a safe place to have it when you have lost your private key or simply memorize it. It is a good idea not to store private keys on your computer because your computer or mailbox can have third party access. Having control over your private keys means you have control over your money or coins.