An angel is a being that was described in the Bible as a messenger of God.
A preacher in 1950s Harlem often quoted Biblical passages about angels. (DS9: "Far Beyond the Stars")
In 2268, Dr. McCoy, expressing frustration at the restrictions of the Prime Directive, joked that he would like to beam down to a primitive planet and say, "Behold, I am the Archangel Gabriel!" (TOS: "Bread and Circuses")
Although he claimed to be "no angel", Miles O'Brien told a Cardassian court in 2370 that he tried to "live every day as the best Human being I know how to be". (DS9: "Tribunal")
Giorgio Vasari considered Leonardo da Vinci to be an angel according to Kathryn Janeway in 2374. (VOY: "Concerning Flight")
A holographic simulation of Lord Byron mention that "It is said the angels themselves take pleasure in their bodies of light." (VOY: "Darkling")
In 2375, Jack claimed that his laws of physics-bending machine "could clip the wings of an angel dancing on the head of a pin". (DS9: "Chrysalis")
As Benjamin Sisko arrived in the Fire Caves for his final showdown with Dukat, his adversary called him "an avenging angel". (DS9: "What You Leave Behind")