The coin of a cryptocurrency performs the same function as units of money do in everyday life. If you pay for something using the US currency, you keep track of how much you’re paying by using the US dollar as your unit of account. Similarly, if you’re paying using Bitcoin, you keep track using BTC. Digital wallets allow you to keep track of your ownership of coins of a cryptocurrency in a similar way we use physical wallets to keep track of our cash. A wallet has two cryptographic signatures: a public address and a private key. The public address is how the cryptocurrency knows where to send a transaction and where it came from. The private key is what allows you to prove that you are the owner of the coins in the wallet. You do this by unlocking the wallet. This can be a different process depending on which wallet you are using: some only require you to set up a password and use the password to unlock the wallet, whereas others may require you to input the private key itself. Once you have unlocked the wallet, you may send coins to another address in a transaction.
There are a few different types of wallets, each one with their own advantages and disadvantages. The most common is a wallet which is connected to the network of the cryptocurrency over the internet. Keeping coins in wallets of this type is known as hot storage. There are other wallets which allow you to keep your coins offline. Some offline wallets come with their own hardware which means your wallet is kept on a separate machine designed specifically for keeping coins away from the internet until you want to spend them. Storage of this kind is known as cold storage. No matter what type of wallet you choose, they all do the same thing: let you store your coins and let you spend them.