In this section the term wallet refers to a Bitcoin or cryptocurrency wallet. Not a traditional leather wallet which you would keep in your back pocket.
Although they are both used to store money the similarity ends there. Unlike a leather wallet which can be lost or stolen from your back pocket, a bitcoin wallet is very secure when used in the correct manner.
A Bitcoin wallet is actually in its most basic form a private key and a public key which are stored on the blockchain. Although you may access your wallet from a hardware device or a desktop wallet, your wallet is always on the blockchain.
To access the wallet you must control the private key. To send money to the wallet you must know the public key.
This is where it can get scary, because if someone gets your private key, or you lose it, your bitcoin may be lost forever. There are many famous cases of people losing millions in bitcoin, you really need to be very careful.
Also every action taken is immutable, so if you send money to the wrong address you will not be able to correct it or have it returned.
Thankfully nowadays hardware wallets make it easier and safer to store bitcoin and other cryptocurrencies. By using them you are less likely to make errors or have your money stolen.