Slashing is the enforcement mechanism in proof-of-stake networks: validators who attempt to attack consensus or fail their duties have a portion of their staked collateral destroyed. Offenses range from minor (downtime) to serious (double-signing, which suggests an attack attempt).
Slashing is what makes proof-of-stake economically secure. Validators stand to lose more than they could gain from attacks. The slashing parameters (how much, for what offenses) determine the network's actual security budget.