Fuzzing is useful for finding bugs that may or may not be serious security issues. If a program crashes when you feed it invalid input, it could potentially crash in a way that allows code execution.

After finding a crash, a researcher will generally explore this to see if it allows for arbitrary code execution. If it does, it is possible for someone to create a weaponized exploit.

For a utility as widely-used as ffmpeg, any bugs pose a threat to many systems. Fuzzing it makes the Linux ecosystem safer for all of us (hopefully).