Off-Chain, as the name implies, refers to blockchain transactions that are processed outside the blockchain.
Due to the limitations of on-chain transactions, including a blockchain’s scalability, speed, and cost, off-chain transactions and Layer 2 protocols were introduced to help Layer 1 blockchains deal with congested networks and slow processing speeds.
They accomplish this by doing the processing work outside of the Layer 1 blockchain network, on a completely different network, with rapid and instantaneous processing, and none of the fees associated with on-chain transactions.
The Lightning Network and Liquid Network are two Layer 2 protocols built on top of Bitcoin that perform off-chain Bitcoin issuance and settlement.
Polygon (MATIC), Arbitrum, Loopring, Immutable X, and xDai Chain are the top 5 Ethereum Layer 2 solutions.