Ever been smacking at a terrapus, when all of the sudden, there was a random explosion that didn't hurt you at all? That was a critical hit -- an extra-strong blow from a melee weapon or tool. Critical hits deal more damage than normal hits. The game will give a small text notification (similar to when you hit a rich vein) each time you make a critical hit.
The higher your combat skill level, the more often you'll deliver critical hits.
If the critical hit is the final blow that kills a mob, and the mob usually drops an item that can be placed (e.g., giblets, fur, resin, guano, scrap metal, etc.), then the item will place itself where the mob died instead of automatically going into your inventory. If the mob normally drops an item that can't be placed (e.g., shillings, jerky, canisters, etc.), then the item will drop into your inventory as it normally would.
Critical hit drops can be mined by anyone, even in protected areas and on protected worlds.