Regions are areas of the world which are considered part of a geographical region. This affects certain mechanics and achievements. Note that certain regions overlap with one another.
Regions can be viewed by clicking a province, then clicking the "regions that include this province" button on the province view. When selecting a region, its boundaries will be outlined in green on the world map.
Steppes
The steppes region is where 
nomadic clans are found. Here, they can fight over pasture land for their herds, and raid the northern branch of the Silk Road for wealth. At the start of the game, most (if not all) nomadic counties are found in this region. Rulers of more civilised government types will have to deal with nomad agitation when trying to expand into this region.
Complete occupation of this region while playing as a nomad is required for the "Steppe by Steppe" achievement.
India
India is where the Indian religions originate. Complete control of this region as a feudal ruler following an Indian religion is required to become the 
Samrat Chakravartin, which awards the "My Very Own Subcontinent" achievement.
The "Jungle" terrain type is unique to this region.
Chinese Region of Influence
This region holds less significance if 
Jade Dragon is not active.
Vicinity of China
Like the Chinese Region of Influence, this region holds less significance if Jade Dragon is not active.
The Near East
This region roughly corresponds to the area known in present times as the Middle East.