Where It All Goes Down
The Rape of the Lock is firmly set in the dressing-rooms and drawing rooms of early 18th-century London and Hampton Court, one of the residences of the Kings and Queens of Great Britain. Everything in the poem—the clothes, hairstyles, card games, modes of transportation, ways of speaking—is calculated to be the hippest, def-est, most fly and up-to-the-moment for the years 1713–1714.
Except, of course, all of those allusions to classical epics (remember, that's what makes the poem a satire; the juxtaposition of the present day with the heroic past).
Politics and Religion
Politically, 1713–1714 (the years the poem was written, revised, and published) were holding-pattern years in Great Britain. The Queen that we meet in Canto III, Anne (who sometimes takes counsel with her advisors, and sometimes takes tea, remember?), was nearing the end of her reign, her life, and the end of her family, as she hadn't had any living children to inherit the throne after her.
Anne's closest relative was her brother, James—but James was in France in exile, because he was a Catholic, and the British refused to have a member of the Catholic faith on their throne. In fact, the entire previous century—the 1600s—had been a time of terrible turmoil and civil war in England, during which Anne's grandfather had been beheaded and all kinds of social, religious, and political transformations had happened. (If you want to read more about Anne's fascinating family, the Stuarts, you can read about them here at the Official Website of the British Monarchy.)
By the 1710s, the British were used to having a Protestant monarch on the throne, and they wanted to keep it that way. So with Anne nearing her end, they were looking around for another of her relatives (NOT a Catholic) to put on the throne (they wound up inviting her cousin, George of Hanover, to come and rule—he is the current Queen's sixth great-grandfather, believe it or not).
Why is this important to the poet Pope and the frilly Belinda and the frivolous Baron? Because all of them were Catholics in Britain at a time when Catholics were under suspicion. People were scared that Anne's brother, James, might raise up an army of sympathizers and come take over, and that all of the Catholics in the country would support that.
It wasn't easy for Pope's or Arabella Fermor's or Lord Petre's family to stay out of political trouble—all the more reason that they needed to stick together and not feud among themselves. So now you see what was really at stake when Pope's friend, John Caryll, asked him to write a poem to "laugh them all together" after Lord Petre snipped off Belle Fermor's hair.
Empire
The early 18th century in Britain was also a time of expanding empire. Anne's generals were very successful in the many wars they fought with France and Spain and the Netherlands, and the nation won a ton of colonies and trading rights to colonies in the Americas and on the coast of Africa.
They already had those thirteen colonies in North America, and they had half of Canada. They'd begun a few outposts in India, and were trading with China, too. You can hear echoes of this imperial expansion in the teas, coffees, perfumes, and decorative items that surround Belinda's daily life.
Science and Medicine
This was also a time when empirical science and the profession of medicine were beginning to gather steam, after the invention of the microscope in the previous century. All of that crazy stuff in Canto IV about the Cave of Spleen? Some of it was Pope making fun of cutting-edge medical research in his day.
As well he might. Another important thing to know about Alexander Pope was the state of his physical health. The poor guy had tuberculosis of the spine when he was six years old, and it stunted his growth and curved his back into a hunch that got worse as he got older. He never grew much taller than four and a half feet (seriously) and he was in massive pain throughout his life. Legend has it the man drank thirty cups of coffee per day. Talk about self-medication. And remember there was no aspirin in the 18th century, kids.