Anthropomorphic animals are animals with humanoid characteristics. The Sonic Series predominantly features this kind of character design, though in-universe they are seldom referred to as such. They are usually referred to simply as the real-world animal they resemble, despite the fact that many non-anthropomorphic animals of the same name coexist with them. Some adaptations have also referred to them as mobians.
"Anthropomorphic animal" or "anthropomorph" is the proper name. "Anthro" is informal. "Mobian" is archaic.
In-universe, the term "Mobian" stems from the many islands1 that anthropomorphic animals originate from historically. the Mobian Isles was an archaic name given to the wide archipelago, which failed to account for how many of such islands existed but were uncharted. Mt Mobius, a gigantic active volcano thought to be at the centre of the isle but in fact only on the outskirts of it, was considered the largest of the anthropomorph-inhabited islands and the point from which the anthropomorphic animals had dispersed. The truth is that the anthropology for these people was poorly understood (even less than the topography of the islands, due to various spacial distortions around most of the islands besides Mt Mobius) and Mt Mobius was far from the largest of the islands anyway.