The Fighters Guild, present across most of Tamriel, provides a common, and more importantly, public place of training and study for those of the warrior persuasion. The guild is a professional organization chartered by the Emperor to regulate the hiring and training of mercenaries, protect commerce, capture or drive away beasts, and similar security duties. Training, goods, and services are cheaper for members.
The Guild gained greater prominence at the beginning of the Third Era under Uriel I. Guild Stewards are entrusted with receiving and dispensing contracts to Guild members, hearing complaints about the servicing of said contracts, promotions, and determining the eligibility for re-admittance into the Guild of former members who had stolen from or assaulted other members. 
The Fighters Guild was conceived in 2E 320 by Versidue-Shaie at the suggestion of Dinieras-Ves "the Iron" to provide for public order without having to resort to standing armies. At first, it was called The Syffim ('soldiers' in Tsaesci). Although it began as an Akaviri-only organization, it eventually opened its doors to all races.
The Guild has been known to suffer from corruption problems in the higher ranks, particularly in Morrowind. The Guild there still performs private contracts, but sometimes deals with disreputable groups. Despite these flaws, the Morrowind Guild near the end of the Third Era succeeded in providing some of the only concrete evidence of the Thieves Guild. At least, they claim to have helped take down an organization by that name which was masterminded by a man called Gentleman Jim Stacey.
The Fighters Guild is highly organized in Cyrodiil and is run by a ruling family, the Dontons. They've had numerous rivals over the years, including the dubious Blackwood Company, and outmaneuvering them has kept the Guild performing at its best.