Ignorance was a quality shared by an individual or society, characterized by their possession of limited knowledge of any of a number of topics, or in general.
Ignorance could be aided by the inability to read. In 2153, Sheriff MacReady preferred that the Skagaran children remain unable to read and thereby remain ignorant of the fact that Humans had initially been dominated by the Skagarans on their colony planet. (ENT: "North Star")
In 2364, when Beverly Crusher tried to protest that her son wasn't told that his actions on Rubicun III were illegal, one of the Edo mediators rebuffed her, claiming they couldn't let ignorance become a legal defense. (TNG: "Justice")
In 2373, The Doctor was surprised to learn that Vulcans knew little about their own sexuality, saying he "fail(ed) to see the logic in perpetuating ignorance about a basic biological function." (VOY: "Blood Fever")
Ignorance was sometimes considered a preferred state of mind, as in the popular saying, "Ignorance is bliss". In 2369, Reginald Barclay mused that this was so in the case of transporters, saying they wouldn't scare him as much if he didn't know how they worked. (TNG: "Realm of Fear")
In 2374, Seven of Nine described Starfleet's Omega Directive, which require the destruction of any detected Omega molecules, as being a product of Starfleet's ignorance and fear. Captain Kathryn Janeway, however, felt that "sometimes fear should be respected." (VOY: "The Omega Directive")