The Mobium is the currency of Mobius. It was established in 1204 when the Mobozone was created from all the states of Mobius. Ostensibly, the creation of a global currency is to facilitate trade and prosperity, but it is another one of Robotnik's methods of ensuring global control.
The Mobium derives its name from the currency established in Sonic Underground and Adventures of Sonic the Hedgehog.
A Mobium can be considered roughly on par with the real-life US Dollar.