"He sure held that bluff till the last second, didn't he, sir? "
"Was he bluffing?"
A bluff was a deception tactic built on an empty boast. It was a common tactic in games like poker, but also had applications in real life. One such example of a bluff applied in real life was the Corbomite Maneuver. (TOS: "The Corbomite Maneuver")
Upon being accused of bluffing, Spock once claimed that Vulcans never bluffed. Worf once made the same claim concerning Klingons, but Geordi La Forge believed this to be a bluff itself. (TNG: "The Emissary"; TOS: "The Doomsday Machine")
In 2269, while the IKS Klothos and the USS Enterprise were trapped in Elysia, the S-2 graf unit of the Klothos suffered damage, but it's captain, Kor, tried to bluff Kirk by pretending they were doing fine. (TAS: "The Time Trap")
Apart from the above-mentioned Corbomite Maneuver, James T. Kirk frequently used bluffs as a tactic. While Kirk and a Klingon crew under the command of Kang were fighting under the influence of the Beta XII-A entity, Kirk threatened to kill Kang's wife. However, Kang called his bluff. During the V'Ger crisis, Kirk tried to bluff the probe, but to no avail. (TOS: "Day of the Dove"; Star Trek: The Motion Picture) The USS Enterprise was equipped with an Inflatable starship decoy, which was intended as a bluff. (TAS: "The Practical Joker")
Kathryn Janeway was also a frequent bluffer. In 2375, Kathryn Janeway tried to bluff Y'Sek, a bounty hunter, but he called her bluff. Confronted with an Class J nebula lifeform in 2376, she successfully bluffed the creature by creating a situation where if it did not cooperate they both would die. (VOY: "Think Tank", "The Haunting of Deck Twelve")
When the USS Enterprise-D was being held hostage by Nagilum, a extra-dimensional creature, in 2365, Jean-Luc Picard responded by initiating the ship's auto-destruct . Nagilum ultimately responded by releasing the ship. (TNG: "Where Silence Has Lease")
In 2375, during the Dominion War, a conflict emerged between Bajor and the Romulan Star Empire concerning the arming of a Romulan hospital on the Bajoran moon Derna. Colonel Kira attempted daring bluff, taking fleet of Bajoran impulse ships to prevent an approaching group of warbirds from reaching the moon, even though they would not be a match for even one warbird. Kira hoped that the Romulans would not dare endanger their alliance with the Federation by firing on the ships. Ultimately it was not the Romulans but Starfleet Admiral Ross who blinked, with Ross threatening to remove the hospital using Federation forces.
During a discussion about Romulan strategy between Mot and Jean-Luc Picard, Mot opined that there's a time when you want to call a Romulan's bluff and there's a time when you don't. Picard countered that one did not always have the luxury. (TNG: "Ensign Ro")
In the Enterprise-D senior staff poker game
For years, the senior staff of the USS Enterprise-D held a weekly poker game every Tuesday evening. As a result, the participants became very good in bluffing each other and calling each other's bluffs.
During a 2368 game , Riker and Beverly Crusher discussed bluffing as Crusher called Riker's bluff only for Riker to predict that Crusher was going to call his bluff again a little bit later, each basing their correct calling of the other one's bluff on "just a feeling". Crusher joked that when Riker bluffed, he raised his left eyebrow in a particular way. (TNG: "Cause and Effect")