Idk if you've watched the prequel films, but I believe Jedi Fallen Order starts right in the middle of Episode 3: Revenge of the Sith. The game really assumes you've watched the film enough to put the pieces together.. But if you just need a recap of the movie to explain what's going on in the beginning of the game, I got you.
Episode 3 Recap up until the game's beginning
There's a war going on between two groups. The Jedi Order and the Clone army vs. the Sith and the Droid army. This has gone on for three years, and the end goal is nearly in sight by the beginning of Episode III.
Anakin Skywalker and Obi-wan Kenobi are two Jedi who have essentially killed two major driving forces of the Sith's side of the war. As this was happening, Anakin was being corrupted by Chancellor Palpatine who's been manipulating the war the entire time in secret. Palpatine's end goal is to find a worthy apprentice who will help him rule the galaxy.
The Jedi Order finds about Palpatine's true identity as the remaining Sith Lord and they fail in attempting to arrest him, Anakin abandons the Jedi ways shortly after, becoming Darth Vader in the process. The Sith have basically won and gotten everything they needed from the war. All that's left is to eliminate the Jedi, which he's capable of doing with the Clones as Chancellor through a surprise attack. Order 66.
It's through Order 66 that the Jedi are mostly wiped out by the time the Original Trilogy begins with Episode 4: A New Hope. Chancellor Palpatine would go on to demonize the Jedi and rebrand the Galactic Republic as an Empire. The droid army is secretly disposed of, and the clones are used to secure the Empire's order in the galaxy. This is how we get Emperor Palpatine and the Stormtroopers.
Jedi Fallen Order's prologue has you playing as a Jedi in training, Cal Kestis. Cal's Jedi Master is presumably a commander for the Clone troopers, and as such, he most likely trains Cal with them in his spare time during the war. The opening level of the game is Cal's training, minutes before Order 66 is issued by Palpatine. He and his Master are being actively hunted down for this reason, and that's why they need to escape.