The canonicity of this location seems about half and half. Originally appearing in Sonic SpinBall, Mt Mobius is the only appearance of either the name 'Mobius', or the Freedom Fighters, in the games themselves, rather than just adaptations or game manual fluff. This would appear to make it incompatible with broader game canon; however, the ladmass itself makes an appearance in the Sonic Origins compilation.1 There also exist official (contradictory) statements on it's canonicity.2
Since the canonicity of the events of Sonic Spinball is questionable, I will not list them in much detail. Note however that, following these events, a failed launch of part ofRobotnik's base on the island, the resultant re-entry was somehow catastrophic to the point of razing the entire mountain down to sea level.
Mt Mobius is one of the outer landmasses in the Mobian Isles, and the first to be discovered by human civilization, according to surviving historical records. Hence, it has traditionally become the namesake of the archipeligo, at least in human culture.
The reason for the late and limited contact made by humans with any of the islands within the archipeligo is the spacial anomalies that have long been observed in the location, effectively preventing human exploration of the islands by traditional human methods until relatively modern times, with the advancement of technology aiding in exploration.
Mt Mobius, like the rest of the Mobian Isles, is located far from the edge of any tectonic plates. However, like nearly every other island within the archipeligo, it anomalously features an active volcano.
Modern theories speculate that these are the result of advanced tectonic bores, created by the Ancient Chao during their terraforming of the isle. It was established by Eggman's occupation of Mt Mobius that, at least that volcano, was ideal for the harnessing of relatively limitless geothermal energy.