Saw Gerrera is a human insurgent from Onderon, leader of the militant faction known as the Partisans, and the character canon uses to ask whether there is a difference between a rebel and a terrorist. He first appears in Star Wars: The Clone Wars episode "A War on Two Fronts" (2012), voiced by Andrew Kishino, and is played by Forest Whitaker in Rogue One (2016) and subsequently in Rebels, Andor and The Bad Batch.
The Jedi taught him this
His origin is the point. In The Clone Wars he and his sister Steela lead an Onderonian uprising against a Separatist puppet government, and their instructors are Obi-Wan Kenobi, Anakin Skywalker, Ahsoka Tano and Captain Rex. The Republic teaches a teenager insurgency tactics as a matter of policy. Twenty years later the Rebel Alliance finds his application of those tactics unacceptable. Both things are true and the material does not resolve them for you.
Too extreme for the Rebellion
By Rogue One he has split from the Alliance, or been pushed out of it, depending on who is describing the separation. He runs cells that use methods Mon Mothma's Senate-facing rebellion cannot be associated with. He has also tortured people, including the Imperial defector Bodhi Rook, using a Bor Gullet — a creature that reads minds and leaves its subjects damaged. The film does not present this as forgivable.
Jyn
He raises Jyn Erso after her mother is killed and her father taken, and then abandons her at sixteen because she has become a liability to him. That abandonment is the wound the entire film is built on, and his reunion with her on Jedha is a genuinely uncomfortable scene: he is delighted to see her, and she is not interested in being delighted.
The body
By Rogue One he is kept alive by an armoured rig, a breathing apparatus and prosthetic legs — visibly a man who has spent decades absorbing damage. Andor (2022) intensifies this, giving him a rasping, wired-in performance and a scene in which he cheerfully lists the incompatible ideologies of the other rebel factions before concluding that he is the only one who is actually a revolutionary.
Why he matters
Because the Rebellion in the original trilogy is morally uncomplicated, and Saw is where later canon put the complication. He is not a villain and the writing never asks you to think he is one. He is the cost of the thing succeeding, kept on screen so the Alliance's cleanliness reads as a choice rather than a given.