Have you ever asked yourself, dear reader, that question? It happens to be the time period in which many of the most popular historical romance novels are set.
What makes it so attractive? Well, I think, there are a number of reasons. The Regency period is roughly from about 1800 to 1820/30. It is called the Regency because it the majority of it is taken up with the time period in England when the Prince of Wales, known to most, but not to his face, as Prinny, ruled. As his father, King George the Third (yes, that George the Third) sunk more deeply into "madness" (probably something more like our today's Alzheimer's Disease) he ability to rule was lessened and his son, the Prince of Wales, was designated by Parliament to rule in his stead.
As the "madness" crept up, and Prinny began to rule, England had just finished winning a long sea war with France. The French Revolution was over, and Napoleon was taking power in France. In England, the Age of the Enlightenment, or Reason, was at an end. Mankind could no longer allow himself/herself, to be ruled by such ideas which left little room for emotion, nature, and God. The French Revolution had been the product of that period, and sometime had to be done to stop Britain from going down the same path.
That something became the Romantic Period in art, literature, and music. It is the period of Beethoven, the Godwins, the Shelleys, Keats, Byron, Coleridge, a period in which many of the old constraints of the society of the Age of Reason were thrown over for the idea that religion, nature, and emotion had a place in the world, otherwise the world would surely go mad, as France had.
This time of conflict of ideas also gave rise to a certain loosening of morals. Some of that was due to the Prince of Wales himself, never known for restraint in such areas. The Napoleonic Wars left the sea and "landed" in Spain, and the British Army was in the thick of it. Men young and old were taking the King's Shilling, and marching off to battle, and many to die, in such places as Salamanca and Badajoz.
Mary Wollstonecraft Godwin had written her treatise on the rights of women, and women were coming more and more to exert themselves subtly in their world. They still needed men for obvious reasons, but they were beginning to understand that they were individuals with minds and abilities of their own.
All of this helps make the Regency such a popular period for historical romance. The loosening of societal norms usually comes along with war and unrest. Women's clothing went from being the overdone styles of the 1700's to the simple lines of the Empire waist (popularized by Napoleon's empress, Josephine), which called for little to be worn underneath. Some women in the English aristocracy scandalously dampened their dresses in front to make them cling to their figures more, outlining much of what was, or perhaps wasn't, underneath. Women began to read, and not just only the gothic romances of the time period, and to write these romances themselves.
All of these conflicting issues made the Regency period ideal for characters in historical romances to fall in love more easily with those whom they should not, to fall into bed more easily, to, and in general, be able to side step society's restrictions until they could work out their own "Happily Ever Afters".
There are more reasons of course, but this is not an historical treatise on the Regency period. It is simply a cataloging of some ideas as to why this period has given rise to such a number of historical romances.