http://fallout.wikia.com/wiki/Brotherhood_Of_Steel
http://fallout.wikia.com/wiki/Outcasts
Basically, the Brotherhood are the decendants of the Military personal, and their families, of Mariposa Military base, near San Fransisco. During the great war, in horror of the FEV experimentation that was going on at their base, they radioed their intention to desert from the US army. When no response or reprocussion came, they moved south to the Lost Hills Facility, where they stayed awhile. Their mission to preserve and maintain technology, and ensure their own survival. They cared little for what happened outside of their bunker unless it directly thretened them (such as the Supermutants and the enclave)
Eventually, schismis in the Brotherhood about direction became great, and the seeming obvious solution was to send the troublemakers out on a quest for technology. A group was sent to the Chicago area, whom lost contact with the "Western" brotherhood of steel, this group formed a facist-style group who also took the name "Brotherhood of steel" (Refered to as the "Midwestern" Brotherhood of steel now, although before FO3 were often refered to as the "Eastern" brotherhood of steel.
For some reason or another, it was decided to be a good idea to send a group of people to the Nation's capital, under Lyon. Upon discovery of a technical wonder (assumed to be Liberty Prime), Lyon recieved a battlefield commision to elder.
Elder Lyons decided that acting benevolently and using their technology to help people and go after the muties was a good idea. The Outcasts weren't happy with this idea, and wanted to keep true to the original brotherhood mission of collecting technology, and apparently neither were the WBOS. The WBOS are seemingly refusing to communicate with both groups.