What does it mean that the retrieval market is “off chain”?
In general the term “off-chain” means that protocol participants don’t send messages to the block chain.
To participate in the retrieval market retrieval miners and clients connect to each other directly in the network and exchange payment, in the form of a payment channel vouchers, for data transfer. If this protocol were “on-chain”, they would communicate with each other indirectly by posting messages to the blockchain that modify the network’s global state machine.
In practice there are usually a few messages sent to the blockchain at the beginning and end of “off-chain” protocols. In the case of the retrieval market participants must set up and close out payment channels. This allows the off-chain payment to be verifiably spendable.