The Ethereum network is a distributed public blockchain network. It is a platform for decentralized applications. It features smart contract functionality.
It is running on a proof-of-work consensus algorithm. And it has a native cryptocurrency called ether.
Ethereum miners are rewarded with ether for each block they mine. They are also rewarded with transaction fees from the transactions included in the block they mined.
Mining ether requires an Internet connection. But once you are connected to the Ethereum network, you can mine ether even if you are offline.
Your Ethereum mining software will keep track of the blocks that have been mined and will submit them to the network when you are online again.
So, you can mine Ethereum without an Internet connection, but you will need an Internet connection to get started and to keep your mining software up-to-date.