The Alien food source appears to be plants. This building provides the perfect balance of light and heat for the Alien plants.
The Food Chamber contains the Aliens' food source in the form of plants. These plants require organic heat and light sources to prevent them from decaying. The Mutant alliance also informs us that a number of Sectoids are held captive within the Food Chamber. Our old enemy has apparently become an Alien delicacy. Whilst the rescue of any Sectoids will guarantee an Alliance with the Mutants, the primary objective is to destroy the Alien heat and light sources as indicated here.
There are smaller bulbs that look a little like the picture around the map, but only ones looking exactly like the picture need to be destroyed. They can be found on top of small structures and in chambers in a large multi-roomed structure. The bulbs explode in a large incendiary blast, so try to be a good 10 squares away when it goes up. They appear highly resistant (possibly immune) to conventional weapons and explosives, but Vortex Mines and Devastator Cannons will make short work of them.