The Carsenome was the base of the Animus. It was manned by its Zarbi servants. The Animus used a long tube in the Carsenome to talk to the First Doctor. The Zarbi took the Doctor's TARDIS there. The Doctor set up communications equipment in the Carsinome on the Animus' orders. Both the Animus and the Carsenome were apparently destroyed by Barbara Wright with the Isop-tope. (TV: The Web Planet)
The Carsenome was not completely destroyed, merely reduced to a single tendril; it regrew as the Animus "beg[a]n again" on Earth, reforming in the London Underground in 1868. The Carsenome was destroyed when Ian Chesterton drove a train into it. (COMIC: Unnatural Selection)
Behind the scenes
The spelling of the Carsenome as "Carsinome" originates from the script of The Web Planet. The comic story Unnatural Selection uses the spelling "Carsenome", Doctor Who and the Zarbi simply refers to it as "the Centre" or "the Zarbi Headquarters", and no other story featuring the Zarbi or the Menoptera mentions it at all.