That is heating grate, left over from an early centralized heating system. The original furnace may have been coal fired and was replaced long ago. The heating duct that connected the furnace to the hole that led up to that grate was removed when the old furnace was replaced. When the house was split into apartments, the old centralized heating system was probably replaced, meaning the old furnace was removed along with the metal ducts in the basement. It would have been too expensive to replace the duct work and grates in the areas of the house above the basement. I'm somewhat surprised that the owners of this house did not reuse these ducts and grates when they installed a newer furnace. Do the individual apartments have their own, much smaller heating system ?