That's just the established naming convention. For brown bears, you have parvorder Ursida, superfamily Ursoidea, family Ursidae, subfamily Ursinae, tribe Ursini, genus Ursus, and finally species Ursus arctos. When there are millions of taxonomic names, you want to establish some kind of regular structure, because you are going to run out of useful distinctive names.
> and finally species Ursus arctos
What happened there? The normal thing would be for the species name to be identical with the genus name, but as far as I can tell Ursus ursus doesn't refer to anything. Why break into Greek?