A cryptocurrency wallet is a device, with a software program or a service which stores the public and/or private keys. This can be used to track ownership, receive or spend cryptocurrencies.
Are my Coins in the wallet?
The cryptocurrency itself is not in the wallet. In the case of Bitcoin and other cryptocurrencies, the cryptocurrency is de-centrally stored. In addition, this is also maintained in a publicly available ledger, called a blockchain. Each blockchain will differ from other cryptocurrencies.
Is it a bank account?
A cryptocurrency wallet can be essentially compared to a bank account, but its your own personal bank account which you have custody over. The only difference is if your wallet is on an exchange (more about that later). The cryptocurrency wallet has a pair of keys, a public set of keys and a private set of keys. The public key allows for other wallets to make payments to the wallet’s address. Whereas a private key enables the spending of cryptocurrency from that address (and you should never ever reveal this).
What types of wallets are there?
Wallets can either be software apps (also called a hot wallet), in the browser or as an app on your phone. They can also be hardware based, which is a usb stick device with a high level of security implemented into it. There is also a Desktop Wallet which is standalone software on your PC. This can also be a copy of the blockchain on your computer called a Node.
Lastly we have a paper based type wallet, where essentially you would print this out to store somewhere. They either store the private key with the user, or the private key is stored remotely and transactions are authorised by a third party. This is the most safest method as it is a total Cold Storage Solution. But you can also loose your funds forever, if the paper gets wet, mould, eaten, burnt or lost.