A pun is a form of wordplay used to show the difference between similar words. It was often used for a humorous effect.
In 2372, after B'Elanna Torres and Harry Kim tried to create a makeshift holo-projector so The Doctor could materialize in engineering, they found that his projection made him appear only a few inches tall. When it was explained that the reason for this was most likely due to the imaging interface not being properly stabilized, and that it was "just a small oversight," adding, "no pun intended." (VOY: "Persistence of Vision")
In 2375, Section 31 chose Doctor Julian Bashir to conduct a mission for them while he was on Romulus by gathering data about the Romulan leadership. The dispatching agent, Luther Sloan, explained to Bashir that "we want you to take the pulse of their government," adding, "No pun intended." (DS9: "Inter Arma Enim Silent Leges")
In 2378, a Federation arbitrator ruled that The Doctor had the ability to control his work, namely his holonovel Photons Be Free, which Ardon Broht published without The Doctor's permission, thus marking a significant victory for the rights of holograms. The Doctor ultimately felt that the decision was a hollow victory and asked the crew of the USS Voyager to pardon the pun. (VOY: "Author, Author")
Later that year, Crewman Chell volunteered to replace Neelix as chef in Voyager's mess hall. Some of the foods listed among his sample menu were Plasma Leek Soup, Chicken Warp Core-don Bleu and Red Alert Chili. Commander Chakotay told Captain Kathryn Janeway that if Chell's cooking was as bad as his puns, they would be in trouble. (VOY: "Endgame")