An ancestor, also known as a progenitor, forebear or forefather, was a generationally distant blood-relative from whom one's family was descended. One's ancestry included the origins of their family or ethnic descent. The study of family ancestry was known as genealogy.
When Doctor Leonard McCoy first arrived in New York City during the early 1930s, he didn't realize he was actually on Earth, so when he first saw someone, he thought he was in a museum or something, and when he met a homeless man, he noticed that he had "good cranial development. No doubt considerable Human ancestry." (TOS: "The City on the Edge of Forever")
The Aldean "Progenitors" built the Custodian, an interactive computer, on the planet Aldea hundreds of centuries ago. These Progenitors prepared the planet with everything that the small colony of Aldeans would ever need. They also supplied a massive power supply, a defensive shield, a repulsor beam and a planet-wide cloaking device. In 2364, with the intervention of the crew of the USS Enterprise-D, the Aldeans re-discovered how the Custodian worked, and began to relearn all their skills. (TNG: "When The Bough Breaks")
While requesting Seven of Nine to assist Kathryn Janeway with historical research on her ancestor Shannon O'Donnel, Seven noted that "This ancestor of yours is fifteen generations removed. You only possess a small fraction of her genetic material. Insignificant." Janeway, explained, that "This isn't about chromosomes [...] It's about character." Later, after Seven had discovered one of the ancestors, Sven Hansen, she explained to Neelix that she doubted Sven had much relevance to her, but Neelix wasn't so sure, explaining that "your ancestors can tell you a lot about yourself," and that more specifically, "there's some of him in you. Just as there'll be some of you in your descendants." It was during this time of family discovery aboard USS Voyager, that Neelix declared April 22nd as Ancestors' Eve. (VOY: "11:59")