The Briar Patch, known to Klingons as Klach D'Kel Brakt, was a region in Sector 441 containing dangerous space matter including the remains of supernovae, false vacuum fluctuations, metaphasic radiation and at least two habitable planets, one of which was a Ba'ku settlement. Ships in the vicinity had to travel at less than one-third impulse power to avoid overheating the vessel's impulse manifolds. The colloquial "Briar Patch" name used in the Federation was first coined by criminal geneticist Arik Soong in the 22nd century, a reference to the Br'er Rabbit of the 1880s Uncle Remus stories written by Joel Chandler Harris of Earth.
In May of 2154, Soong suggested the cloud as a hiding place for himself and a group of Augments aboard a stolen Klingon Bird-of-Prey, but his suggestion was rejected by Malik, the self-appointed leader of the Augments. (ENT: "The Augments")
In 2271, the region was the site of the celebrated Battle of Klach D'Kel Brakt, where Dahar Master Kor led the Klingon Empire in a glorious victory over the Romulan Star Empire. Nearly a century later, Kor was still fond of re-playing the battle in holosuites. (DS9: "Blood Oath")
By the 24th century, the region was part of Federation space. In 2375, the Briar Patch was the scene of the Battle of the Briar Patch between the Federation starship USS Enterprise-E and Son'a ships, following the discovery of a plot to relocate the Ba'ku. (Star Trek: Insurrection)
The names of the Briar Patch's stellar contents and neighbors originates from a computer-displayed okudagram which Geoffrey Mandel created for Star Trek: Insurrection. While not clearly seen on-screen, the graphic was reproduced in The Secrets of Star Trek: Insurrection (p. 143) by Terry J. Erdmann.
For Insurrection, the appearance of the Briar Patch was developed by Mark Wendell, CGI supervisor at Santa Barbara Studios, and Art Director Richard Kriegler. "Our goal was to make this area of space look like a big nasty rat's nest, filled with gases and clouds and so forth," Wendell explained. (The Secrets of Star Trek: Insurrection, p. 26)
According to Geoffrey Mandel's non-canon reference book Star Trek: Star Charts (p. 56), the Briar Patch was located in the Beta Quadrant. However, the Star Charts (p. 63) also depicts Klach D'Kel Brakt as being a Klingon planet near the Romulan border, since the book was released before "The Augments" aired.