Something that's putrescent has begun to decompose or rot, like the putrescent remains of the broccoli at the very back of the vegetable drawer in your refrigerator. Ew!
When things are putrescent, they're starting to become putrid — rotten and stinky. Everything that decomposes eventually becomes putrescent, from the remains of your lunch in your locker to the dead fish on a beach after a big storm at sea. This colorful way to say "spoiled" or "rancid" comes from the Latin putrere, "to rot," and its root, putris, "rotten or crumbling."