On-Chain, as the name implies, refers to blockchain transactions that exist on and have been verified to the blockchain by miners or validators.
On-Chain also means that transactions have been recorded to the blockchain.
On-Chain transactions get shared with all of the nodes of a network, as they have been verified and confirmed.
The opposite of an On-Chain transaction is an Off-Chain transaction, which is processed outside of the blockchain, by a second-layer protocol, normally for lower costs and faster confirmation times.