DSC S1E03 - Context is for Kings

On her way to a prison colony, Burnham's shuttle is damaged and rescued by the USS Discovery. Her captain quickly conscripts Burnham to assist in a mysterious experiment. She is now surrounded by a crew that doesn't trust her, and working for a captain she doesn't entirely trust. What is the Discovery really working on, and more importantly, why is this show set 10 years before TOS and not 100 after VOY???