"Outie" is a term used for the severed — specifically the "home life" self, as opposed to the work life “innies.” While innies are meant to spend their entire existence at work (excepting the case of Gabby Arteta) and have no memory of anything outside of it, outies live in perpetual weekend. With most of Lumon Industries’ severed employees, this means outies lose consciousness on the elevator going down to the severed floor and gain consciousness on the same elevator going up, after work is over.
When a person chooses to undergo the severance procedure, severing their memories between work and home and creating two distinct “selves,” the outie is the self that remembers making the decision and continues to choose to send their innie to work, but actually exists before and after work and on weekends. Outies have power over their innies in this regard: they chose to create them, and they can terminate them by quitting their job or retiring if desired.
Conversely, outies also have a strange sort of power over their employers. While Lumon Industries, for example, can mistreat their innies in basically any way they wish because they’re unable to tell the outside world about it, they can't exactly torture their outie forms or give them any reason to be suspicious of their jobs. This is because, unlike innies, outies can quit their jobs and deprive Lumon of its workforce or take any grievances to the press. This leaves it up to Lumon to make sure they never want to.
This is done by blocking communication between innies and outies and sometimes telling outies outright lies. For instance, when Mark S. is injured on the temple after Helly R. lobs the speaker at him during her orientation, Lumon instead tells Mark it was from slipping on an overhead projector slide and gives him a gift card for his troubles. The outie Mark has no way of verifying this and the innie Mark is unable to speak for himself, so outie Mark doesn't quit his job and the mistreatment continues.
Despite the unbalanced power dynamic between innies and outies, both are ultimately subjugated by their employers and both are deprived of a meaningful life. Not only do outies lose eight hours of consciousness a day to their innie, effectively cutting short their own lifespans, many presumably undergo severance under difficult circumstances. A bereaved and alcoholic Mark chose severance as an attempt to get over his wife's death, though, as many have pointed out, all he's really doing is making his days shorter. And Helena is severed as a PR stunt after presumably being pressured by her father, who is doubtfully a loving and healthy parent.