In general, the term “off-chain” pertains to transactions that happen outside a blockchain network. Transactions of such nature work through the swapping of private keys to an existing wallet instead of transferring funds. This could also work through the use of either a third-party or a coupon-based interlocutor.
Users benefit from off-chain transactions as it comes with lower fees, has the capability of being transacted immediately, and bears more anonymity compared to on-chain transactions.
The method that the user chooses to employ determines whether or not off-chain transactions may eventually be recorded on chain.