The Brotherhood of Steel is an important organization in the Fallout games (Fallout, Fallout 2, Fallout Tactics) from Interplay. Black Isle made 1 and 2, and 14° East made Tactics. If you intend on playing these games at a later time (which you definitely should if you haven't already), maybe it's best you found out about the BoS on your own.
The Brotherhood is a militaristic organization who has taken it upon themselves to bring order to the chaos of the post-nuclear wasteland of 22nd+ century America. They realize that technology is the only hope for humanity and civilization, and they actively search out and research new technologies that could help further their ends. The Brotherhood typically will make pacts with the various townships and cities throughout the wastelands: protection from Raiders and other aggressors is given in exchage for a certain percentage of the eligible population as Brotherhood recruits. Some people are resentful of this policy, while others gratefully accept it and join willingly.
Formed by a group of survivors from a military Vault near San Francisco, the Brotherhood maintains a network of bunkers throughout the wasteland. These bunkers are typically large, high-technology, underground buildings with research facilities, barracks, and equipment storage. The Brotherhood's most important technology is Power Armor, a strength-enhancing, highly protective type of armor powered by it's own miniature nuclear reactor.
There are 5 groups of members within the Brotherhood, listed here roughly in order of importance:
- Initiates: The initiates are newly recruited soldiers, fresh from the wasteland. They haven't yet chosen their calling within the Brotherhood, and are given simple chores and quests to test their abilities.
- Scribes: These members are interested in learning and science. Scribes make up the Brotherhood's researchers, historians, and intelligence experts. They are typically clothed in orange robes.
- Knights: the Brotherhood's equipment experts. The Knights do some fighting, but mostly keep track of and repair the weapons, armor, vehicles, and other equipment kept by the Brotherhood. They are the quartermasters and mechanics. They usually wear metal armor.
- Paladins: Elite fighting troops. They are battle-hardened warriors, almost always wearing Power Armor. The Paladins often specialize in specific areas (sniping, heavy guns, thrown weapons, demolition, etc). When the Brotherhood has an important combat mission, it's the Paladins that do it.
- Elders: Original survivors from the Vault, and their successors. The governing core of the Brotherhood. The movers and the shakers, they make all decisions.
Joining the BoS is optional (I think) in Fallout 1, but pretty important, 'cause that's where you get the Power Armor. I'm pretty sure it's mandatory in Fallout 2. In Fallout Tactics you start in the Brotherhood as an initiate. Almost everybody in the BoS is a terminal hardass. The Brotherhood is portrayed by Fallout's wonderful sense of satiric humor as a reincarnation of the military, disembodied from a government to fight for. | 
