Puberty was the development of secondary sexual characteristics as found in most humanoid species, as well as the development of the ability to reproduce. The secondary sexual characteristics vary greatly from species to species.
Elogium was the Ocampan equivalent to puberty, while jak'tahla could be considered the Klingon form of puberty. (VOY: "Elogium"; Star Trek: Insurrection)
The finiis'ral was a stage in a Kriosian empathic metamorph's life that was similar to late-stage puberty. (TNG: "The Perfect Mate")
While on Miri, Spock mentioned the possibility that the native children could contract the life prolongation project virus when they entered puberty. (TOS: "Miri")
Rybo-viroxic-nucleic sequences and structures was one of the key factors that controlled certain chemical and genetic changes in development during puberty of a humanoid. (TNG: "Rascals")
When Odo began experiencing fluctuations with his morphogenic matrix in 2372, Doctor Julian Bashir theorized that the fluctuations were the result of a normal biological process for Changelings that was similar to puberty and menopause. Odo replied that Bashir's theory was "interesting", but suggested that the doctor keep it to himself. (DS9: "Broken Link")
In 2374, Tom Paris welcomed Chakotay and Seven of Nine in a cave on a class Y planet where he was trapped and told them he saw his life passing before his eyes and arrived at puberty when he lost consciousness. (VOY: "Demon")