Putridness is a state of decomposition or decay. You can guess at something's putridness by the way it smells — just stick your nose in that lunch bag you left in your locker over spring break to gauge its putridness.
The putridness of the rotting cabbage you found in the back of the fridge might turn you off of coleslaw permanently. Yuck! This noun is also used colloquially to mean "gross" or "awful," so you might complain to your friends about the putridness of the pizza at that new place on the corner. The root of putridness means "to rot or to stink," so you're basically saying, "That pizza stinks!"