This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
The term Red Angel originated with Spock, who claimed to have encountered it during his youth, and was later adopted by the crew of Discovery, which had been tasked with studying the red burst phenomenon. Its appearance could not be linked to any known winged or avian lifeforms in the Federation, and a mind meld between the figure and Spock revealed emotions of loneliness and desperation. (DIS: , "Point of Light", "An Obol for Charon", "If Memory Serves")
The Red Angel was the culmination of temporal research started by Section 31 in the 2230s, after it was discovered the Klingons were doing the same. It was capable of allowing a single pilot to travel through time with the assistance of a time crystal via micro-wormhole. Because of the inherent instability of these, the suit generated a graviton beam that was designed to hold the wormhole open, allowing the traveler to return to the point from which they left. The suit left in its wake an anomaly that generated tachyon radiation. The technology was on the verge of being tested by Section 31, when it was thought to have been destroyed by the Klingons on Doctari Alpha. (DIS: "Saints of Imperfection", "The Red Angel")
Chronologically, the Red Angel was first observed on Earth in 2053, at the East Fork Presbyterian Church in Richmond, Indiana, during the height of World War III, by a group of soldiers and civilians who took refuge there after overhead jets began dropping nuclear weapons in the area. A mysterious entity, "surrounded by pillars of fire", entered the building, bringing the church and everyone in it thousands of light years away to the planet Terralysium unharmed. (DIS: "New Eden")
They survived on the planet for two centuries, and created a religion which ascribed religious importance to the entity. Investigating a red burst in 2257, Captain Christopher Pike and an away team visited the planet where Amesha shared the story of the Red Angel with them. Pike later obtained the helmet camera video footage, which showed a red, angel-like figure. (DIS: "New Eden")
Spock, as a child, claimed that the Red Angel had spoken to him on several occasions, most notably when it told him where to find his foster sister, Michael Burnham after she tried to run away from home. Amanda and Sarek had always assumed that Spock used logic to find Burnham and wrote the Red Angel off as a figment of Spock's imagination, an opinion Amanda reconsidered after being shown more reports of the angel in the late 2250s. (DIS: "Point of Light")
After some investigation, and admittance by Section 31 that the suit was theirs, the figure was captured by a combined team of USS Discovery and Section 31 personnel. The Angel was de-activated by a electromagnetic pulse, and trapped in a confinement field. After the suit was de-activated, the pilot fell to the floor, and was identified by Michael Burnham as her mother, thought killed in the Klingon attack on Doctari Alpha nearly 20 years prior. (DIS: "The Red Angel")