Layer 2 is the generic name given to a variety of projects dedicated to scaling the use of the Ethereum network. As we know, Ethereum is a decentralised, peer-to-peer blockchain network. However, the very properties which make Ethereum open and trustless, also lead to a limit on the speed at which it is able to process transactions.
This problem arises due to the large number of participants (i.e. miners) required for block validation in the Proof of Work consensus mechanism. In practice, the Ethereum 1.0 network can currently support only about 30 transactions per second, which is much smaller than what a large-scale system serving the public would require.
Ethereum 2.0 and the transition to Proof-of-Stake should improve things, however, with the rapid adoption of decentralised finance, it is unlikely to be enough on its own.
Layer 2, then, focuses on solutions which are capable of satisfying transactions off the main Ethereum blockchain. To retain the security properties, these solutions offer novel mechanisms which still use the main chain to prove their validity. Examples of Layer 2 solutions in development include (zk- and Optimistic) Rollups, and Sidechains (such as the Polygon network).