Mar-Vell was a rogue Kree scientist posing as Carol's friend Dr. Wendy Lawson on Earth. She was using the Tesseract to develop a Lightspeed Engine to save the Skrull race from extermination by the Kree.
Yon-Rogg demanded the Asis' power source, which he believed was the Asis' engine itself. Presumably, the Kree also wanted the Lightspeed Engine technology Mar-Vell had invented and planned to give to the Skrulls.
It was clear why the Skrulls wanted it; they were being exterminated by the Kree and needed faster-than-light travel so they could find a new planet as far away from the Kree as possible, and Mar-Vell, who believed it was an unjust war, was betraying her own people to help them. However, the Kree already had interstellar travel and an armada, so what was the value of the Lightspeed Engine to them?
This comes down to the somewhat ill-defined rules of space travel in the MCU. In Captain Marvel, and in the Guardians of the Galaxy films which are set decades later, interstellar travel happens by the use of Jump Points - the hexagon-shaped barriers in space ships fly through. They're essentially artificial wormholes, not unlike the wormholes that lead to and from Sakaar in Thor: Ragnarok. What Mar-Vell invented was the MCU equivalent of warp drive in Star Trek and jumping to hyperspace in Star Wars, which would allow ships to travel faster-than-light without the use of Jump Points, by harnessing the power of the Tesseract, which was really the Space Infinity Stone.