The Batarians were once a council race who came into conflict with the council when humans began colonizing areas of space known as the Skyllian Verge. The area was believed by the Batarians to be in their own protected areas, and conflicts between humans and Batarians began. The council sided with humanity on who had the right to colonize where, and the Batarians angered by this decision, removed themselves from the Citadel and are now only found outside of Citadel Space in the Terminus Systems.
Batarian society is based on a caste system. Trying to cross one's caste boundaries is strictly prohibited. Batarians believe that they are superior to other races because they have four eyes. They usually show this by tilting their head to the right during a conversation. Slaves are used as cheap labor. To gain more slaves, slaver groups (which usually consist of Batarians attack colonies and force everybody captured into slavery for the rest of their lives.
The Batarians seen in in areas such as the Terminus system are not representative of the average Batarian average citizens are forbidden to leave Batarian controlled systems by its government. The ones seen by Commander Shepard are criminals that were either exiled by the Batarian government or managed to slip out via illegal means. The government is assumed to be a paranoid dictatorship because of the tight hold it has on its citizens and it constantly blaming all of its woes on humans. Despite this, they government still issues updated linguistics dictionaries, though this is mostly to distribute propaganda to other species. The government also runs the only Batarian weapon manufacturing company, Batarian State Arms.
The Batarian government secretly supports and funds slaver and pirate raids against human colonies. One of the biggest pirate raids against human colonies, the Skyllian Blitz, was actually a proxy war done by the Batarian government because the colonies attacked were hotly contested between Batarians and humans. However, the raid failed and the humans managed to take over the area. In Citadel space, Batarians are a very little threat to other species because of the amount of military forces in it, but in more lawless parts of space, such as the Terminus System, there is a very real threat of being attacked by Batarians if one lives on a colony.