FBX is Autodesk's proprietary 3D interchange format, originally built for Kaydara's FilmBox motion-capture tool (hence the name) and acquired by Autodesk in 2006. It carries meshes, materials, rigs, skeletal animation, blend shapes, cameras, and lights in one file, which made it the de facto asset format for game engines: Unreal Engine, Unity, and Epic's Fab marketplace all ingest FBX as a first-class citizen. Two encodings exist, binary (common) and ASCII, both versioned; modern tools write FBX 7.x.
How to open
Unreal Engine and Unity import FBX directly. Blender opens it via File > Import > FBX. Autodesk's free FBX Review (Windows/macOS) previews files without a full DCC install. Maya, 3ds Max, Cinema 4D, and Houdini all read and write it natively.