OB getting his nickname by telling Loki the thing that Loki told him in episode 1 certainly goes along with the meaning of Ouroboros. However, we really get the full blast of the snake eating its own tail in episode 4. If you recall, when Victor Timely (Jonathan Majors) was taken to OB’s office in the Time Variance Authority (TVA), he recognized OB as the person who wrote the TVA handbook that Ravonna gave him in the mid-19th century. OB says he learned everything he knew from “a brilliant 19th-century inventor named Victor Timely,” saying he could have been bigger than Einstein if he’d had the equipment. Then OB realizes that Victor is that very inventor.
It isn’t just brain-addling for the audience. Loki wonders aloud about OB’s work being based on Victor’s and Victor’s work being based on OB’s, with OB actually saying, “It’s like a snake eating its own tail!” Then they want the other to sign their TVA handbooks and Sylvie (Sophia Di Martino) finally calls an end to the weird time loop fan club. It’s a very funny scene, slowed down only by Major’s sort of Captain Kirk-style speech pattern, but what does it mean for the show and the MCU?