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 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")
In September of the same year, Mary Reed told Captain Jonathan Archer, while they were having an on-screen discussion which Archer took in his ready room, that the Reed family had been "navy men" for generations. (ENT: "Silent Enemy")
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")
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")