Poker was a card game of chance and skill which originated on Earth. The main aim of the game was for players to wager on the strength of their cards, in relation to the cards held by the other players. If a player believed they held a greater "hand" than another player, they could "call" them on it.
During the USS Enterprise's encounter with the Fesarius in 2266, the Enterprise was threatened with destruction. Lt. Commander Spock suggested to Captain James T. Kirk that they had been "checkmated", Kirk took the gaming analogy to find a "bluff" from poker that they could use against the Fesarius. Spock was fascinated by the game of poker and Dr. Leonard McCoy vowed to teach it to him. (TOS episode: "The Corbomite Maneuver")
Strangely enough, Kirk once again uses his skills in 2267, but under less intense circumstances. In the aftermath of the nearly-derailed Babel Conference, he enjoyed a session with Sarek in sickbay. The captain was rehabilitating from his knife wound; as the ambassador recovered from open heart surgery. From their long hours of recoup time, they found a way to pass the time in a logical, yet amusing way. They made makeshift poker chips from tongue depressors and used whatever cards they could find. Much to both Spock and McCoy's amazement. Sarek even coined the human vernacular, "Come to Poppa," after winning a hand. (ST novel: Federation)
In the 24th century, Starfleet crews would hold a floating poker tournament when five or more Federation starships were at a given location at the same time. As a young man, Starfleet officer Jean-Luc Picard lost a month's wages betting on the tournament shortly after his promotion to Lieutenant. As there were going to be five starships at Luxor IV, the crew of the USS Enterprise-D looked forward to playing in and winning the match. The Enterprise was diverted when the Devil's Heart was rediscovered, and unable to play in the tournament. However the USS Venture's crew was able to participate since they had put into port at Luxor IV to repair a baffle plate malfunction. (TNG novel: The Devil's Heart)
In the 2360s and 70s, the command staff of Enterprise-D played a poker game every Tuesday night, Captain Jean-Luc Picard had a standing invitation to this event but did not participate until 2370 following an encounter with Q. (TNG episodes: "Cause and Effect", "All Good Things...") In 2367, honored guests Ambassador Spock and Adm. Leonard McCoy competed with the Enterprise-D crew. Chief Miles O'Brien learned much to his (and Dr. Selar's) suprise that winning and bluffing had much to do with the "Vulcan poker face". Being the best in the galaxy, supposedly. (TNG comic: "The Modala Imperative") For part of 2370 this game was played on a Friday night. (TNG novel: Dragon's Honor)
In 2365 Wesley Crusher ran a holodeck program in which he was a participant in the senior officers game. He played a successful hand and did so with expert unreadability before he had to end the program after being called to the transporter room. (TNG comic: "Space Seeds") This same year, Lt. Worf earned from Cmdr. William T. Riker the nickname "Ice Man". For winning two consecutive hands, while maintaining his cool and keeping and icy bearing each time. In Worf's Klingonese, the word is d'akturak. (TNG episode: "The Measure of a Man", DS9 episode: "Blood Oath")
From 2368 to 2369, Data's years of honing this skill came into good use as he won against Frederick La Rouque and Joe Falling Hawk. Data also had a talent for dealing cards in a rapid shuffle; a credit from his android reflexes. Data was known to compete with holographic programs as well. (TNG episodes: "Time's Arrow", "A Fistful of Datas", "Descent")
"Texas Hold'Em" was a poker variant, where community cards were used by all players to make the best hand. Christine Vale regularly played Texas Hold'Em while serving aboard the USS O'Keefe. (TNG novel: A Time for War, A Time for Peace)