Rotten Food is what food becomes after it has spoiled. The 'freshness' of food is identified in the tooltip.
Soon after becoming 'almost too rotten to eat' the food will turn into Rotten Food and become inedible. There's currently no use for rotten food, it can simply be thrown away.
Food can be prevented from rotting by storing it inside a refrigerator. This will stop the rotting process until it's removed from the container.
Below are the decay states as stated in the food tooltip from most fresh to almost rotten.