Anticipation
Notifies all trainers upon entering battle if an opponent has a super-effective move, Self-Destruct, Explosion, or a one-hit KO move.
Full effect
When this Pokémon enters battle, if one of its opponents has a move that is super effective against it, Self-Destruct, Explosion, or a one-hit knockout move, all participating trainers are notified. The move itself is not revealed; only that there is such a move. Moves that inflict typeless damage, such as Future Sight, and moves of variable type, such as Hidden Power, count as their listed types. Counter, Metal Burst, Mirror Coat, and one-hit KO moves to which this Pokémon is immune do not trigger this ability.
In game description
The Pokémon can sense an opposing Pokémon's dangerous moves.
Pokemon with Anticipation
Using Anticipation in Cobblemon
Abilities are passive and always active, so Anticipation costs you nothing to run. If it is marked hidden on a species above, expect it to be harder to obtain: servers differ in whether hidden abilities come from breeding, an Ability Patch, or events.
See the Pokedex for which abilities each species can have, and IVs, EVs and breeding for how to actually pass one down.