"Off-chain," as opposed to "on-chain," is a technical term referring to blockchain technology. A piece of technology that is "off-chain" is something that affects how a blockchain manages storage space, processes transactions, or similar functions, but exists as an external piece of technology that does not directly influence the blockchain. In other words, an "off-chain" software function is something that "plugs into" a blockchain to improve its technical capabilities - sort of like how an external hard drive or USB stick improves the memory management capabilities of a desktop computer - as opposed to altering the structure and/or function of the blockchain itself. An example of off-chain technology is the Lightning Network.
- Fraud proofs — Secure on-chain scalability. Hackernoon.