A Pokémon with Anticipation will "shudder" upon entering battle if an opponent has a move that is super-effective against it or a One-Hit-KO move (such as Fissure, Horn Drill, Guillotine, or Sheer Cold). This ability only activates when the ability-bearer switches in, not when an opponent switches in.
Anticipation does not activate for moves with variable types, like Hidden Power, Judgment, or Weather Ball, even if they would be super-effective.