The Composer is a really overpowered piece of technology. It basically looks like a small gyroscope with a ruby-like crystal in the centre. It can do anything, from changing the chemical makeup of anything, to destroying anything at the molecular level. Over the course of Galactic History, there have actually been three Composers, although only one is considered to be the true Composer. The other two are named the Prothean Composer and the Promethean Composer.
The Original Composer was created by an unknown species that dates back billions of years, even before the Precursors. Its first recorded use was by the Precursors as an experiment to create life, and it ended up creating Cybertron and all its inhabitants as well as their power source, the Allspark. It then went missing for thousands of years after the Precursors died out thanks to Forerunner rebellion.
The device was found by the mysterious Ratakans, also known as the 'Builders', who used it to create a huge space station called the Star Forge, before their empire collapsed and they were reduced to a primitive society inhabiting the planet Lehon (actually Rakata Prime), around which the abandoned Star Forge, with the composer still inside, orbited for nearly 5000 years.
Around the same time, a superweapon that would later become the Promethean Composer was being constructed by the Didact on Requiem, as he hoped digitising biological flesh was the key to stopping the Flood. The plans for the Composer were assimilated by the Forerunner Domain following an encouter with a Prothean Vessel, and whilst he lay dormant, the Didact had instructed his Prometheans to build a Composer using plans stored in the Forerunner Domain that had been taken from the Precursors.Darth Malak and his boss Revan (Who is in no way related to Rarth Devan) two years after the end of the Mandolorian Wars. These two Jedi used it to make huge fleets of warships, and attacked the Republic with this newfound power. However, thanks to the efforts of Trask Ulgo and his buddy Devan, the Star Forge was accidently destroyed above Rakata Prime during a circus performance a mere 4 years after being rediscovered. The Composer, however, survived, albiet in a superficially damaged state.
Meanwhile, the plans for a new Composer were found by the Protheans during the Reaper Invasion following an encouter with a long-abandoned Forerunner Gateway. The Protheans started to build their own model of Composer with a different function in mind, believing it to be a superweapon which could be used to wipe out the Reapers. However, their efforts failed because they all died before they could finish building it. The Prothean Composer that they had been constructing disappeared, but the plans remained.
Centuries later, the Didact's forces recovered the actual Composer, which had been in orbit around Rakata Prime for centuries, drifting in amongst a ring of debris from the final battle of the Rise of Trask Ulgo - fragments of Sith and Republic ships as well as the remains of the Star Forge itself. The Prometheans returned the Composer to Requiem, and transported the Promethean Composer that the Didact had built himself onto Installation 03.
Meanwhile, the Prothean Composer was relocated by the crew of the SSV Normandy and was the saving grace for the forces of the Galaxy during the Reaper War, during which it was used as a weapon against the Reapers. The Humans, during the Thirty-Eight-Hundreth Battle of Earth, fired out a big blue energy pulse from the Composer (Known as The Crucible at the time) which shut down all Reapers in the Galaxy as it travelled through the Mass Relays. When the Reapers reacitvated, they were suddenly friendly to everyone and offered to help rebuild. However, the inferior design of the Crucible meant that it was blasted into oblivion in the process - or so everybody thought. It was in fact taken into the Medusa Cascade, a time-altering nebula, and was used by the Daleks to house their crappy Reality Bomb, before being unceremoniously blown to smithereens by a Time Lord/Human biological meta-crisis that grew from The Doctor. Of the three Composers that exist, the Prothean version was the first to be destroyed.
Nearly 500 years after this, back on Requiem, the Didact was attacked by Jorgey who bullied the Didact into giving up the real, original Composer, which Jorgey then used to reconstruct New Reach and build his race of Reachites. This meant that the Didact had to slog his way to Installation 03 to recover the crappier Promethean Composer that didn't work properly at this point. However, he didn't seem to care, all he wanted to do was disintergrate Humans. It was then destroyed by Johnny using a HAVOK nuke. The Promethean Composer was therefore destroyed, eliminating the last of the copy Composers, leaving Jorgey's the last one in existence.
The original Composer is currently still under the protection of League Lord Protector Jorgey, who only authorises the use of the device to terraform the many barren planets in the Galaxy. Since the plans for the Composer still exist within the Forerunner Domain, it is rumoured that Cortana, having linked with the Domain, has created more. None shall ever be as powerful as Jorgey's Composer, however, so the majority of League species need not worry.