Sturdy allows the Pokémon to survive with 1 HP if attacked at full HP with an attack that would otherwise knock it out. It also prevents One-Hit-KO moves (Fissure, Horn Drill, Guillotine, or Sheer Cold).
If Sturdy activates before the final hit of a multi-hit move (such as Fury Swipes), the subsequent hit will still deal damage and cause the Pokémon to faint.
Sturdy does not prevent self-inflicted KO moves such as Selfdestruct, Explosion, and Final Gambit.