A generation was a group of related individuals all belonging to a specific time period. The term could also refer to the time period itself.
Some technology was also referred to as belonging to a generation; that is, a certain number of designs removed from the original.
In September that year, (citation needed • edit) Mary Reed told Captain Jonathan Archer, while they were having an on-screen discussion in Archer's his ready room, that the Reed family had been "navy men" for generations. (ENT: "Silent Enemy")
From 2000 to 2374, Shannon O'Donnel, an ancestor of Kathryn Janeway's, was fifteen generations removed. Seven of Nine did not see the relevance of Janeway's interest in such an ancestor, as she "possess[ed] a small fraction of her genetic material." (VOY: "11:59")
In 2268, Spock estimated that "assuming one tribble, multiplying with an average litter of ten, producing a new generation every twelve hours over a period of three days," the total amount of tribbles on Deep Space Station K-7 now amounted to 1,771,561, also taking into consideration how much quadrotriticale they had eaten and the volume of the storage compartment they were inside. (TOS: "The Trouble with Tribbles")
In April 2151, while debating the qualities of Humanity with T'Pol, Charles Tucker III mentioned that the Human race had "pretty much" eliminated war, disease and hunger in less than two generations, a situation which Tucker expressed he wouldn't describe as small potatoes. (ENT: "Broken Bow")
On the planet Terra Nova, the descendants of the SS Conestoga colonists, the Novans, built an immunity against the radioactive fallout of an asteroid impact in 2083 for generations and took shelter in underground tunnels and caves for the next three generations until 2151, when a landing party from Enterprise NX-01 relocated them to the southern hemisphere. Also embedded in the Novans for two generations was the idea that Humans had destroyed their colony. (ENT: "Terra Nova")
When the USS Enterprise was attacked by a thermonuclear warhead that was launched from the planet Ekos in 2268, Leonard McCoy commented that such technology was "generations ahead of where these people should be technically." When he wondered aloud "How'd they manage that?" James T. Kirk thought that "Maybe they had help." Later, Isak, a member of the neighboring Zeon race, described that his people's "warlike period ended dozens of generations ago." (TOS: "Patterns of Force")
In 2374, when Julian Bashir was visited by his fellow genetically-engineered friends from the Institute – Jack, Lauren, Patrick, and Sarina – they calculated that United Federation of Planets defeat by the Dominion was inevitable, but that a rebellion (centered on Earth) would arise after five generations and that the next generation after that would succeed in overthrowing Dominion rule. (DS9: "Statistical Probabilities")