Slashing
The automatic destruction of part of a validator's staked deposit as a penalty for provably harmful behavior.
Slashing is triggered by evidence that a validator signed two conflicting messages, such as two blocks for the same slot or contradictory attestations, and anyone can submit that evidence to the chain, which applies the penalty without human involvement. On Ethereum a slashed validator is also ejected from the active set, and the size of the penalty scales with how many other validators are slashed around the same time, so an isolated operator error is inexpensive while a coordinated attack or a correlated infrastructure failure is severe. This correlation penalty is why running the same keys on two machines for redundancy is dangerous and why validators are advised to spread across clients and hosting providers. Delegators who staked through an operator share in the loss, since the penalty comes out of the deposit their stake backs.
In practice
Running the same validator keys on a backup machine at the same time as the primary can produce two signatures for one slot, which is a slashable offense even though no attack was intended.
The common misunderstanding
Being offline is not slashing; downtime costs small inactivity penalties, while slashing requires provably contradictory signatures.