"On-chain," as opposed to "off-chain," is a technical term referring to blockchain technology. A piece of technology that is "on-chain" is something that directly affects how a blockchain manages storage space, processes transactions, or similar functions. Examples of this include increasing the block size of a blockchain, or sharding.
On-chain also refers to transactions involving cryptocurrency that involve moving the cryptocurrency from one wallet to another and are thus recorded on the blockchain.
- Fraud proofs — Secure on-chain scalability. Hackernoon.