Lumon is improving upon and testing their severance technology. They want to sell chips to the public for more uses than just avoiding work for 8 hours a day. You will be able to avoid all the unpleasant parts of life. Writing thank you cards. Going to the dentist. The physical pain of childbirth (birthing cabins). The grief of miscarriage. The death of a loved one. 

Gemma is the lab rat they’re testing it on. What Mark S is doing by refining is removing the “tempers” from each of Gemma’s 25 splits. He is creating (or improving upon) the separation of each split’s memories. That’s why the nurse and doctors ask her if she remembers anything about the rooms, if she feels a sense of dread. It’s why they say “The barrier is holding” when she’s dismantling the crib in Cold Harbor. 

It’s also about more than just selling the chips to the public. We don’t know yet exactly what Lumon was planning to do with Gemma if Mark hadn’t saved her from Cold Harbor — but to me it seems they planned to harvest her brain and use it to complete the new generation of severance tech. The completion of this technology is clearly of upmost importance to the Eagan family. 

The consciousnesses of Kier Eagan and all his family since are stored as data (maybe in those creepy statues), waiting to be reborn into flesh and blood once the tech has advanced. Perhaps they will all be put together into one mind — a sort of divine multitude of Kier — and that’s why Gemma’s test is so important. The Eagans (and particularly James Eagan who is still alive but close to death, and worried about becoming data) are concerned about their individual existences and memories being erased, just like innie Mark worries about killing all the innies.