The 1inch Limit Order Protocol allows for conditional execution of orders based on price discovery formulas, with arbitrary callbacks that can execute actions before funds are debited. It defines an order structure with a signature, amounts, and a threshold. Orders are executed by first validating the signature and checking if the timestamp and nonce conditions are met, then calling getMakerAmount/getTakerAmount and executing any callbacks before transferring funds from the maker's account. The protocol interacts with smart contracts to validate signatures and execute the order.