In the novel Edit
Nothing is known of Ofglen's life prior to the beginning of Gilead; Offred does not even learn her real name. When Gilead took over, Ofglen became a Handmaid. However, she secretly joined Mayday as well, to bring down Gilead from the inside.
Meeting Offred Edit
Ofglen is assigned to be Offred's partner whenever she leaves her home to go shopping and walking. Ofglen plays the part of a pious and dutiful Handmaid, so as not to arouse suspicion, as she is unsure if Offred is a true believer in the regime. Upon learning she is not, Ofglen extends friendship to Offred and tells her about Mayday. Ofglen tries to get Offred to gain information on her Commander, stating that he is one of the most prominent members of Gilead's government.
Towards the end of the novel, Ofglen attends a Particicution with Offred and attacks the condemned, a man accused of rape. Ofglen viciously kicks him in the head until he falls unconscious, and later explains to a horrified Offred that the man was no rapist but a member of Mayday, and that she had knocked him out to spare him an agonising death.
Ofglen is eventually discovered to be a member of Mayday, but hangs herself when she sees the Eyes coming for her. She likely committed suicide to avoid betraying her comrades under torture. Offred is later informed of her fate by Ofglen's successor, who is also called Ofglen.
In the TV series Edit
In the television series, Ofglen is portrayed by Alexis Bledel. Compared to the novel and the film adaptation, she is given more of a backstory and her eventual fate is altered. Her real name is stated to be Emily.
Offred initially thinks of her new shopping partner Ofglen as “pious little shit with a broomstick up her ass”. As she is walking home with Ofglen, the latter expresses sympathy for what happened to Moira. Offred tentatively reveals she knew Moira both at the Red Center and in the time before. The two women end up outside a clothing store, which Ofglen reveals was once an ice cream parlour. When she claims the ice cream was “better than good sex”, Offred realises Ofglen is not a true believer in the regime after all. Ofglen in turn reveals she always thought the same of Offred, saying that Gilead is good at turning women against each other. Offred tells Ofglen about her family and failed escape attempt, whilst Ofglen in turn reveals she had a wife and son, Oliver, who fled to Canada. At the gate of Offred’s house, Ofglen warns Offred that an Eye is a member of her household.
When she is walking with Offred on the way back from grocery shopping, she reveals that she used to be a college professor, teaching cellular biology. She was also in a same-sex marriage, which made her a huge target for the regime. While most college professors and "Gender Traitors" were sent away for their "sins," she says she was spared because she has "two working ovaries." She also reveals that she and her wife had a son together, whom she speculates would be five years old during the series' timeline. She tells Offred that her wife and son had Canadian passports and thus were able to escape while she herself did not. She also reveals she is a member of Mayday, though she does not refer to the resistance group by name.
Shortly after revealing her true self to Offred, she is removed from her home and replaced by another Ofglen. The previous Ofglen was apparently caught having a sexual affair with a Martha. A trial is shown in which the Martha is sentenced to death for her crimes while Ofglen is sentenced to "Redemption", meaning that she was spared because "God had seen fit to make her fertile." The Martha and Ofglen are then loaded into a van where they hold hands until they arrive in a yard. There, Ofglen's Martha lover is forcibly removed from the van and Ofglen is forced to watch as she is hanged. Ofglen is then taken to a medical facility, where she undergoes a forced clitoridectomy to destroy any future enjoyment of sex.
Ofglen is later reassigned and named Ofsteven. Offred meets with her and expresses sorrow for what was done to her. She tells Offred her real name of Emily, and also says that she should join Mayday, finally referring to the organisation by name, adding that she could help the fight to stop Gilead. At a marketplace with Offred, she steals a car and manages to drive away before running over a Guardian. She is then forced out of the car by the other Guards and led into a black van. 
Her future fate is unknown, whether she will be spared or executed. It may be possible that she may be sent to the Colonies for killing a Guardian.