An extended public key (xpub) is a public key that can create other public keys.
Xpubs are used to build wallets. The plain public keys produced from them are used to build the addresses for the wallet.
Singlesig wallets use just one xpub, and each address for the wallet is built with just one plain public key. Meanwhile, multisig wallets are created with one xpub from each master private key (or seed phrase) that's involved. Multisig addresses are built with one plain public key from each xpub.
For example, when you upload two xpubs from two hardware wallets to Unchained, this allows you to build a multisig vault with your two keys and the Unchained key, and that vault can produce unlimited unique addresses.
Xpubs are not private keys, and they cannot give someone permission to spend funds. Instead, they are used for building wallets, viewing wallet balances, and receiving bitcoin into the wallet.
If you want to learn more, one of our engineers Justin Moore has an insightful write-up on xpubs that might be of help. We also have another article about the various components of a bitcoin wallet, including xpubs, plain public keys, and addresses.