Invulnerability is a cheat that can be obtained after beating the game and revisiting The General's Lair. If on Fur Fighters: Viggo's Revenge, you will need to rescue all of the babies.
As its name suggests, you are invincible to damage. Despite the name, you are not invulnerable to high falls or auto-fluffs (i.e. getting crushed, failing to get out of the shuttle liftoff on time in VAB Building, etc).