First, an excerpt:
Another gate delivered them into the second court, grass-grown, and more wild than the first, where, as she surveyed through the twilight its desolation—its lofty walls, overtopt with briony, moss and nightshade, and the embattled towers that rose above,—long-suffering and murder came to her thoughts. One of those instantaneous and unaccountable convictions, which sometimes conquer even strong minds, impressed her with its horror. The sentiment was not diminished, when she entered an extensive gothic hall, obscured by the gloom of evening, which a light, glimmering at a distance through a long perspective of arches, only rendered more striking. As a servant brought the lamp nearer partial gleams fell upon the pillars and the pointed arches, forming a strong contrast with their shadows, that stretched along the pavement and the walls.
-- The Mysteries of Udolpho, 1794.
Crumbling castles, brooding noblemen, virtuous women terrorized by supernatural wickedness in the darkness. These are all part of the the early tradition of Gothic fiction. Fixated on atmosphere, the Gothic tradition, particularly at the height of the Georgian (and Regency) era, was a mix of horror, melodrama, and romantic elements. Whenever Gothic fiction is considered, there's one woman who helped define the genre: Ann Radcliffe.
While not the first author to write what we would now consider a Gothic novel, she helped popularize it and brought Gothic novels into the literary mainstream. For this reason, she's often considered the true definer of the genre.
Although she was wildly successful during her lifetime, she wrote only a book of poetry and six novels: The Castles of Athlin and Dunbayne (1789), A Sicilian Romance (1790), The Romance of the Forest (1791), The Mysteries of Udolpho (1794), The Italian (1797), and Gaston de Blondeville (1826). If you're wondering about the large number of years between her fifth and sixth novels, the last was actually posthumously published by her husband.
Her works tended to focus on virtuous and imperiled heroines of breeding dealing with the aforementioned brooding noblemen, mysterious exotic castles, and supernatural elements. Radcliffe, however, in contrast to many other Gothic writers was rather explicit (with one exception, Gaston de Blondville, though as noted above, it would only be published after her death) in showing that the supernatural elements in her stories all actually had rational, non-supernatural explanations. One of the continuing elements in her works is a heroine desperately resisting an onslaught of emotion and instead, eventually, applying reason to the situation. For the time, especially given many people's sentiments about women in general, this was actually somewhat feminist. It was, however, a type of feminism considered mostly acceptable by late Georgian and Regency society. Indeed, her combination of sensible heroines, lack of true supernatural elements, and virtue allowed her brand of Gothic novels to be acceptable for the literary mainstream. Critics at the time hailed her as the "mighty enchantress" and praised her work.
Surprisingly, at the height of her popularity at the age of 32, she stopped writing. As she kept a rather low personal profile, it's not certain her exact reasons for quitting, but many literary historians attribute it to her personal disgust with the direction Gothic fiction was taken, particularly in terms of prurient disreputable supernatural content. For example, The Monk, published in 1796, gained some popularity. The novel features, among other things, rather negative portrayals of female characters, demon pacts, rape, and incest.
Though Radcliffe stopped writing before the true Regency era, her works remained popular and influential throughout the 19th century both in England and the United States. As many of the authors she influenced later went on to influence others, her Gothic tentacles stretch rather farther than many people might expect from a woman with a relative modest number of works.
Her 19th-century popularity is easily attested by the direct references to her works in Regency and later fiction. One of the more famous and familiar to modern readers would be the several references to her work, particularly The Mysteries of Udolpho, in Jane Austen's Northanger Abbey (1817), a parody of many elements popular in Gothic fiction and Radcliffe's books. I should note that Ms. Austen was not the only one parodying Gothic excess at the time.There was a veritable cottage industry of Gothic parodies.
So, whenever you read a book where some young woman is running down a spooky mansion/castle corridor or watch a similar movie, it may very well be a descendant of Radcliffe's work.