The Daedalus Project, or Project Daedalus, was a classified time travel research project developed by Section 31 around the 2230s, after it was discovered that the Klingons were researching time travel. Considering this a critical threat, Section 31 found itself in a temporal arms race, and the project was aimed at gaining a strategic advantage.
The project came to light when a file with the name "Project Daedalus", was implanted into Lieutenant Commander Airiam's augmented systems. Just before her death, Airiam urged Michael Burnham to find the project. (DIS: "Project Daedalus", "The Red Angel")
The Red Angel
The key component of the suit, a time crystal, proved hard to procure. A young Section 31 operative named Leland learned from an operative on the Klingon homeworld Qo'noS, that one such crystal was being sold on the black market near an Orion outpost, and managed to steal it. The time crystal was brought to Doctari Alpha, where a scheduled nearby supernova would provide the energy for a test. However, the Klingons tracked the crystal, and attacked the outpost. The Burnhams, stationed on the outpost by Leland, were believed killed in the attack, which was later described as a Klingon terror raid. (DIS: "The Red Angel")
Section 31 believed the project lost until 2257, when they learned that the entity known as the "Red Angel" was apparently using the Daedalus suit, which was confirmed when the "Red Angel" was revealed to be Gabrielle Burnham. (DIS: "Project Daedalus", "The Red Angel")