A morgue unit was a storage compartment for keeping dead bodies in refrigeration, serving much the same purpose as a morgue, though a lot smaller. This type of technology had a control panel atop the unit, which could be used to open a drawer built into the unit.
In 2153, a morgue unit was used to store an incinerated Xindi-Reptilian corpse in a Starfleet hangar. Admiral Forrest opened the drawer in the unit so that he, Captain Jonathan Archer, and Vulcan Ambassador Soval could view the charred Xindi remains. (ENT: "The Expanse")