TL;DR: A crypto wallet stores a private key that gives you access to your crypto on the blockchain and makes it simple to buy, sell, receive, and trade crypto assets.
Your crypto wallet is your password to accessing your funds. It stores your private keys, which unlock your funds to be moved away from the wallet, and ensure you are the only one granted access. Crypto wallets come in many formats:
Your crypto wallet is your digital bank account on the blockchain. The main difference between this one and your bank’s, is that this one cannot be accessed by a third party: you are your own bank. Regardless of the format they come in (hardware, online, or on a piece of paper), wallets all perform the same functionality. The password they contain (private key) manages the control to your funds by being proof that you are the rightful owner (through a digital signature). If you lose your private keys, you lose access to the funds in the wallet.
An important thing to note about your crypto wallet is that it doesn't store your crypto, your crypto assets live on the blockchain and your crypto wallet holds the private key that lets only you access those assets as the private key proves that you own those assets. If you lose your private key, you lose your assets which is why it's very important to keep it as secure as you can.
Each crypto wallet comes with two keys:
Wallets come with a seed phrase that allows them to be recovered in case they are lost. Seed phrases are strings of randomized words (i.e. world shape apple mug…) that when combined unlock access to the wallet. The seed phrase should be stored in a safe place, and preferably not digitally (as this can be susceptible to hacks).