Bok was a Ferengi captain (or DaiMon), who first appeared in the Star Trek: The Next Generation first episode "The Battle." He later made a second appearance in the seventh season episode "Bloodlines."
A successful captain and businessman, Bok had earned himself a substantial fortune by the time of the early 2350s. He also had a single son, Flax, who followed him into business and likewise, achieved the rank of DaiMon. In the year 2355 the USS Stargazer, under the captaincy of Jean-Luc Picard, unwittingly entered the territory of the Ferengi, who at that point were still mostly unknown to the Federation. Determined to prove himself, Flax launched into an unprovoked attack, crippling the Stargazer within minutes. Before the Ferengi ship could finish off the Stargazer however, Picard improvised a tactic subsequently known as the "Picard Manoeuvre," using the ship's warp drive to travel much closer to the Ferengi ship, which was temporarily confused by the appearance of two Stargazers and attacked the after-image from the ship's original position. The Stargazer destroyed the Ferengi ship, though the manoeuvre burned out its already-damaged power systems, forcing the crew to abandon ship.
Bok answered his son's distress call, but found only the destroyed remnants of Flax's ship, and the wrecked Stargazer, with no sign of its crew. Bok used the ship's log to determine that Picard was responsible for his son's death, but to his frustration was unable to take any direct form of revenge due to the Ferengi Alliance's isolationist policy toward the Federation. He continued in his own career, while plotting revenge all the while.
First encounter with Picard
Early in the year 2364 the Ferengi ended its isolationist stance toward the Federation, finally allowing Bok to put his plan into action. Having had the Stargazer repaired in the interim, he invested most of his fortune into two Thought Makers, illegal devices that allowed a victim's mind to be controlled. He placed one in the captain's quarters of the Stargazer, which he then presented to Picard, now in command of the USS Enterprise-D, under the guise of improving relations between the Federation and Ferengi. Picard unwittingly took the Thought Maker onto the Enterprise, and Bok began remotely using it to inflict pain on Picard, and then causing him to hallucinate his previous battle with the Ferengi. Bok also placed a falsified Captain's Log in which he admitted attacking the Ferengi ship unprovoked, in order to lead the Enterprise crew off-track.
Eventually, Picard was compelled to beam himself aboard the Stargazer, where Bok revealed his motives. He then forced Picard to relive the battle fully, and placed the Stargazer under his control, knowing full well that the Enterprise would likely be forced to destroy the Stargazer, and believing that even if Picard somehow destroyed the Enterprise he would then be executed by the Federation for his act of mass-murder.
Just before Picard could launch his attack on the Enterprise however, its crew showed Bok's first officer, Kazago, the second Thought Maker as proof of Bok's motives. Realizing how dangerous his captain had become, Kazago removed him from command on the ostensible grounds that he had not intended to make a profit from the mission.
Second encounter with Picard
Bok was dismissed from his position as DaiMon, and left financially destitute. Six years later, he had come into enough money to try revenge against Picard once again, purchasing an experimental subspace transporter and hiring a surgeon to resequence the DNA of Jason Vigo, the son of Picard's former lover Miranda Vigo, in an attempt to make it look like Jason was really Picard's illegitimate son. After threatening Jason and forcing Picard to take him aboard the Enterprise for his protection, Bok taunted Picard several more times, before eventually snatching Jason away with the transporter.
As Bok made preparations to torture Jason to death, the Enterprise crew (who by now had also figured out that Jason and Picard weren't actually related at all) figured out how to duplicate his subspace transporter, and Picard beamed himself aboard Bok's ship. Moments later one of Bok's hired crew indirectly revealed that Bok hadn't paid them anything up-front and had instead promised them part of a "ransom" that he knew full well he wouldn't be receiving. Outraged at not only being lied to, but also being an unwitting party to an attempted murder, Bok's crew decided to hand him over to the authorities instead, reasoning that their only chance of getting anything from the mission was a reward for stopping a dangerous renegade.