Romance
If a novel is called Something-or-Other: a Romance, you can feel pretty confident that it's a romance of some kind. But of what kind?
Towards the end of Possession: a Romance, Roland Mitchell has an unusually meta moment of realization: "He was in a Romance, a vulgar and a high Romance simultaneously, a Romance was one of the systems that controlled him, as the expectations of Romance control almost everyone in the Western world, for better or for worse, at some point or another" (23.66).
When Byatt refers to "vulgar" and "high" Romance here, she's thinking of two distinct literary and cultural forms. By "vulgar" Romance, she means something along the lines of Harlequin romance novels or Fifty Shades of Grey. By "high" Romance, she means old-fashioned quest narratives: tales of wonder and derring-do by heroes like King Arthur and his knights, or something like Tolkien's Lord of the Rings.
Possession is a "high" Romance in the sense that it's a quest narrative, and it's a "vulgar" Romance in the sense that it's a love story. Got it? Good.