Layer 2 stands for a secondary framework or protocol that is built on top of an already existing blockchain. These layer 2 solutions aim to solve the issues regarding transactions speed and scalability. Big blockchains like Bitcoin or Ethereum are still not able to process thousends of transactions per second (TPS), and this is certainly a negative aspect regarding their long-term growth.
In this context, the term 'layer 2' refers to multiple solutions that are being proposed to the scalability problem blockchains face. The most popular layer 2 solutions are probably the Bitcoin Lightning Network and the Ethereum Plasma. Both of these solutions are striving to help increase the throughput to blockchains.
Generally speaking, layer 2 protocols create a secondary framework, where blockchain transactions and processes can take place on their own and not on the main chain (layer 1). Therefore these solutions are also called 'off-chain' scaling solutions.
A positive effect of layer 2 solutions is that the main chain does not need to undergo any structural change because the second layer is added as an extra layer. This helps with achieving higher throughput without putting the network security at risk.
A big portion of the work that would be performed by the main chain can be moved to the second layer. While the layer 1 provides security, the second layer offers high throughput.