Life Support is responsible for two things; keeping breathable oxygen in the ship, and more importantly, brewing coffee for the engineer.
While powered the life support will provide oxygen to the ship, and brew coffee for the engineer. If the Life Support is not powered, oxygen will slowly drain from the ship, and cause a game over if it reaches 0%.
The more power provided to the Life Support, the quick the ship will fill with oxygen.
By interacting with the Life support and taking a coffee the engineer can refill his stamina bar, used for sprinting.