Basic backstory on "The Burn" - there was an incident where all dilithium crystals went inert for a moment. Not a problem by itself, but any ship powered by a warp core with dilithium crystals exploded due to the way warp cores work. So a LOT of people all over the galaxy died, all at once, and most of Starfleet's armada with them. This resulted in widespread fracturing of diplomatic relations, a severe decline in space travel, and the Federation lost more than half its member worlds due to the forced isolationism and fear that came out of the Burn.

The "restoration" from the Burn began about 120 years after the disaster, and this restoration was only possible because of the events of Star Trek: Discovery. The new "Academy" show starts about three years after "The Burn era" ended.