1 [definition]
Method of storing cryptocurrency where the private key is secure, and at least 1 public key is available.
The crypto assets exist on the blockchain, so wallets only need to store and present a way to interact with them. This is done by storing the private key and using it to interact with the blockchain, and using the private key to derive public keys which assets can be sent to
2 [types]
Wallets come in many forms. The most common of which are are software (applications, web), and hardware wallets. Each type has it's uses and have their own advantages and disadvantages. Generally, hardware wallets are ideal for long term storage, and mobile/extension/software wallets are ideal for daily use.