A nanite is a microscopic molecular machine, most often used to alter or manipulate the inside of living cells.
Nanites were responsible for the legendary healing properties of the Ilaiyen Archipelago. This nanotechnology had been given to the Ilaiyenai by extra-planetary explorers sometime prior to or during the 13th century. (TOS short story: "As Others See Us")
In 2366, Wesley Crusher experimented with nanites, causing them to evolve into sentience. After threatening the computer core of the USS Enterprise, these nanites were transported to planet Kavis Alpha IV to create their own civilization. (TNG episode: "Evolution")
In that same year, Elias Vaughn and Ruriko Tenmei used trillions of nanites to find and unwrite the code of Cren Veruda's artificial intelligence, which the Borg had found at Uridi'si. (DS9 novel: Lesser Evil)
In 2376, Simon Tarses used medical nanites to treat injuries that Ro Laren suffered after Taran'atar's attack. They were able to limit the genetronic matrix's activity at the molecular level and prevented accidental metastasization. (DS9 novel: Warpath)