A network is an Ethereum environment. This is where users test, develop, and interact with others.
The Ethereum Mainnet is the base blockchain where on-chain transactions occur. When you send ETH to a friend's wallet on the Ethereum network, you're using the Mainnet. This is also referred to as Layer 1.
Layer 2 networks are where off-chain transactions occur. As the name suggests, Layer 2 networks operate on top of Layer 1. These networks reduce the cost, and time, of transactions. Optimism, and Arbitrum are examples of Layer 2 Networks.