The "Battle of Maxia" was the rather grandiose name bequeathed by DaiMon Bok to a ship-to-ship combat between the USS Stargazer, commanded by Captain Jean-Luc Picard and what was (at the time) an unknown alien vessel. In 2355, in the Maxia Zeta star system, this vessel attacked the Stargazer without warning or provocation, severely damaging the Stargazer.
Captain Picard ordered his helm to obtain a bearing on the other ship, and upon receiving that bearing ordered his ship to momentarily jump into high warp. He then ordered the ship to come to a full stop near the unknown ship. As a result, the Stargazer briefly appeared to be in two places at once - and the alien vessel fired where the Stargazer had been. The Stargazer fired phasers and six photon torpedoes at the ship, which exploded (killing the entire crew). The desperate maneuver Picard used at the battle would come to be known as the Picard Maneuver.
Despite surviving the combat, Stargazer was critically damaged, on fire, and losing power. Captain Picard decided the only way to save his crew was to abandon ship, and did so. After several weeks in escape pods and shuttlecraft, the Stargazer crew was rescued by Starfleet.
It was not until 2364 that DaiMon Bok revealed to Captain Picard and the Federation that the unknown alien ship was a vessel of the Ferengi Alliance, the Seventy-Fifth Rule. Bok would later reveal that the attacking ship had been commanded by Bok's only son, Flax. Having found the derelict Stargazer in a decaying orbit around Maxia Zeta V, Bok refurbished it in an attempt to take revenge against Picard for the death of his son before being exposed and relieved of command by his first officer. (TNG episodes: "The Battle", "Bloodlines", TNG novel: The Buried Age)