We're not talking about goth kids and their weird vampire romance stuff. That's not the definition of a Gothic Romance in literature. No Buffy and Angel here.
Gothic Romance refers to a style of literature that arose in the 1700's and lasted until the early 1800's. These works flourished in many parts of the western world, including England and Germany. Black Forest mythos, for example, and medieval castles were popular subjects.
Just picture strange and macabre stories, often with elements of horror. An old monk, a castle, a ghost, a skeleton, a mystery, a foreboding old baronic mansion, that sort of thing.
The word "romance" had a different meaning before the 20th century. It often meant a story with some adventure, some mystery, something out of the ordinary. When a person led a boring life, if something happened to them it was often called a romance. An element of love was common but not necessary. Seafaring books of adventure such as Victor Hugo's Toilers of the Sea were classified as romance.
Gothic is an often misunderstood word, but has come to mean so many things. For literature, a good starting place is medieval architecture as viewed from the eyes of the 18th and 19th century. By that time, the old castles and churches were already described as "ancient" and "hoary" (that's a nice old-fashioned word), implying a great age and feeling of mystery. The word that may best describe the intended mood or feeling of Gothic literature is "grotesque". Not necessarily meaning gross or gory as we think of it today. It meant something unusual with a hint of the macabre.
I'm not going to give some elaborate explanation of the topic, I wouldn't do it justice. Plus, I haven't read much Gothic Romance, yet. I will know more after reading/reviewing a few of them. But the info is out there if you want more details. Wikipedia has a ginormous page about it, with details only a lit major could love.
After I finish 19th century classics and get to the Gothic Romance period, I'll start with The Mysteries of Udolpho, by Ann Radcliffe (1794). It's very long and (so far) a bit rambling with little direction towards whatever the main plot will turn out to be. But more on that later.