Plain meaning
Start with the shortest useful explanation before going deeper.
A nullifier is a cryptographic value derived deterministically from a compressed account's leaf hash (and optionally a secret) that is published and recorded on-chain when that compressed account is consumed (spent) in a state transition, permanently marking the account as used and preventing it from being spent a second time in a double-spend attack. In Light Protocol, nullifiers are inserted into an on-chain nullifier queue account and periodically batch-processed by Forester nodes into a nullifier set stored in a separate Merkle tree, allowing the validity proof to assert both that the input account exists (inclusion proof) and that its nullifier has not yet been recorded (non-membership proof). The nullifier scheme allows compressed accounts to be treated as UTXOs — each account is consumed once and replaced by one or more output accounts — while maintaining the privacy and succinctness properties of the ZK proof system.