Validator slashing is another name for slashing: the penalty by which a proof of stake network confiscates or destroys part of the tokens a validator has locked up, when that validator breaks the protocol's rules in a way that threatens the network. The main entry explains the offences, the size of penalties and how they are applied on different networks.
The longer phrase simply makes clear who is punished. It is common in institutional settings, where firms that stake clients' assets, or that buy staking services from an operator, need to describe the risk in contracts, risk registers and disclosures. Typical triggers are signing two conflicting blocks or votes, often caused by running the same validator keys on two machines at once. Being offline usually brings smaller penalties that are not slashing in the strict sense.
Because the loss falls on the staked assets, it is passed on to those who delegated them unless the operator has agreed to cover it. Institutions therefore look at an operator's key management, its use of distributed validator technology, and any insurance or indemnity offered. Holders of a liquid staking token share slashing losses across the pool.