The Battle of the Briar Patch was fought between the USS Enterprise and two Son'a battle cruisers in 2375. The Son'a cruisers attempted to prevent the Enterprise from informing the Federation Council about a conspiracy to forcibly relocate the Ba'ku. They were defeated via an unorthodox maneuver by acting Enterprise captain William T. Riker.
Investigating a "malfunction" in Lieutenant Commander Data during a mission to the Ba'ku planet, the Enterprise crew discovered a joint plan between Starfleet Admiral Dougherty and Son'a Ahdar Ru'afo to relocate the Ba'ku population. Once the Ba'ku were evicted, the Son'a would deploy a collector to harvest the life-rejuvenating metaphasic radiation from the Ba'ku planet's rings, rendering the planet uninhabitable for generations.
Captain Jean-Luc Picard was outraged that Starfleet would condone a plan that deprived the Ba'ku of their rights. He ordered his first officer Commander Riker to take the Enterprise out of the Briar Patch and alert the Federation Council, while he and several of the command staff remained on the planet to forestall the deployment of the collector. Ru'afo, well-aware his plans would be jeopardized if revealed to the Federation public, told Dougherty that he could have his ships intercept and "escort" the Enterprise back. Despite knowing the likely outcome, Dougherty reluctantly consented to the action.
The two Son'a battle cruisers closed on the Enterprise when it was still an hour's travel from the edge of the Briar Patch. Riker had Lieutenant Daniels inform them that the Enterprise's transceiver assembly was down and that they could only send messages, not receive them. The Son'a responded with a photon torpedo. Riker ordered the Enterprise to full impulse, even though it would damage the engines as the impulse manifolds had not been properly outfitted for the Briar Patch. The Enterprise began "burning deuterium" as it traded fire with the Son'a.
One of the Son'a cruisers detonated an isolytic burst behind the Enterprise, creating a subspace tear. As the Enterprise's warp core was acting like a magnet to the tear, Chief Engineer Geordi La Forge recommended ejecting the core and detonating it to hopefully seal the tear. Riker gave the order, though La Forge had already carried it out by then. The resulting explosion impacted the Enterprise, causing heavy damage. Since there was nothing preventing the Son'a from firing another burst, Riker realized that he had no choice but to confront the Son'a to complete his mission.
As the Son'a cruisers outgunned the Enterprise, Riker had the Bussard collectors gather volatile metreon gas to "shove it down the Son'a's throat", which La Forge dubbed the "Riker Maneuver". Taking personal control of the helm via the manual steering column, Riker flew the Enterprise in front of the Son'a and released the stored gas just as the lead cruiser prepared to fire. The Son'a ignited the gas, causing a massive explosion that destroyed the lead cruiser and propelled its debris into the second, disabling it.
With the battle won, Riker successfully contacted the Federation Council and was assured that the Ba'ku relocation would be halted pending a top-level review. He then brought the Enterprise back to the Ba'ku planet in time to disable Ru'afo's flagship and retrieve Picard from the collector. (Star Trek: Insurrection)
Some observations and suggestions about how the Battle of the Briar Patch was depicted in the first draft script of Star Trek: Insurrection were made by the executives at Paramount Pictures, in a memo sent to the "Star Trek team" on 3 December 1997. The comment was: "We would like Riker’s battle with the two Son’a ships to be as riveting as any Star Trek battle to date [....] Because the Son’a are not yet much of a threat, this battle is not particularly dramatic. Also, because the ships are moving slowly, the battle does not seem that thrilling. What would happen if Riker jumped to warp, or full impulse power in the Briar Patch?" The document then proposed that the battle might conclude with a maneuver that ultimately became the Riker Maneuver. The memo ended: "However the battle is choreographed, this should be a defining sequence for the movie." (Fade In: The Making of Star Trek Insurrection)