To get a better understanding of what a private key in Ethereum is, you need to understand what Asymmetric cryptography is. https://en.wikipedia.org/wiki/Public-key_cryptography
There are two popular asymmetric cryptography algorithms. RSA and ECDSA. Ethereum uses ECDSA (Elliptic Curve Digital Signature Algorithm). You can see how ECDSA functions here. https://blog.cloudflare.com/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/
To put the above in perspective in simple terms - A private key is a very large random number that is used to generate a public key. This public key is your address on the Ethereum blockchain. The private key allows you to sign transactions. These transactions can be verified by other participants on the chain against your Public key.
To better educate yourselves, use the link below to generate your private key on your own machine and derive your address on the Ethereum network.
Now a private key is very hard to remember, so wallets allow you to store your private key in them secured with a password (using symmetric cryptography). What this means is, you can sign your transaction on that same wallet instance using an easy to remember the password. It is very important to understand that this password is not your private key, and if you lose access to this wallet, your password will not allow you to retrieve the private key from other wallets.