A Resyk Center is a place where the Meat Wagon takes corpses and recycles the nutrients from them, which is then turned into food for human consumption.
Resyk Centers are essentially places that make thinly veiled cannibalism possible, but it's the only option since there is no farmland in the Mega-States. In the end, every human corpse is totally recycled, whether it be for food, manufacturing or organ donation. This prevents both farming and burial.
From the "A-Z of Judge Dredd": "Nothing goes to waste in Mega-City One, not even the dead. Due to the massive population of the city, and incredibly close confines, burying the dead is a privilege reserved for the super-rich. Most corpses are sent to the nearest Resyk centre, where the body is broken down into its component parts, and rendered into other materials. Funeral services are frequently held at Resyk so the bereaved can say goodbye to their loved ones, and purchase reasonably priced souvenirs at the gift shop."
In the 2012 Dredd film, when Judge Lex mentions that Mega City One is "a... meat grinder" this is both literal and figurative.