The TruthYou will live again as a part of me...
The following will contain spoilers, especially regarding the events of Final Fantasy Seven, and eventually, Final Fantasy: Advent Children.
Sephiroth was led to believe that he was born of a woman named Jenova, and never knew who his father was. Growing up, he realizd that he was special, and different from other people, though he never knew how different he was.
Actually, Sephiroth was the child of both Lucrezia / Lucretia and Hojo, the assistant to gast, who spearheaded the JENOVA project. Hojo impregnated his assistant Lucrezia, who loved him (though whether or not she was willing or unwilling is unknown), and then injected JENOVA cells into her unborn baby. When Sephiroth was born, Lucrezia was irrevocably changed by the serum. SOLDIER Vincent Valentine, who loved Lucrezia, tried to save her, but Hojo defeated him, injecting monster serum into his body. Sephiroth was later sent to Midgard, raised under the watchful eye of Shinra.
As early as about fourteen to sixteen years old, Sephiroth was already inducted into the ranks of SOLDIER, a powerful fighting organization of Shinra, Inc., and in approximately ten years was known as the most powerful SOLDIER. Soon, he took another SOLDIER who showed promise under his wing, named Zack.
Five years before Final Fantasy Seven, Sephiroth and Zack were sent out to investigate monster attacks happening around the town of Nibelheim; specifically, to investigate the Mako reactor in the mountains surronding the town. Both were accompanied by a young escort guard named Cloud Strife, and had commissioned a tourist guide named Tifa Lockhart to lead them into the mountains.
Upon arriving at the reactor, Sephiroth was stunned to see numerous pods there, each containing human beings injected with monster serum, transforming them into beasts. He also found a sealed room containing the word, "JENOVA" on the door - the same name his mother was supposed to have. Shocked, and wondering if he was subjected to the same experiments on these monsters by Gast (although Hojo was actually the instigator) Sephiroth shut himself in the Shinra library for three days, reading all he could about JENOVA and the Ancients. He learned that the JENOVA project was designed to create the perfect super-SOLDIERs, and that he was the first of these.
Angry and betrayed, Sephiroth burned Nibelheim to the ground, and then set off to the Nibelheim reactor to free his "mother", JENOVA. He killed Tifa's father, and then severely injured Tifa, Zack and Cloud. Underestimating the then-escort guard's abilities though, Sephiroth was stunned when Cloud mustered the strength to throw him into the Mako Pit, along with JENOVA's head. Sephiroth was missing after that and thought to have died. In the meantime, Shinra covered up the incident, and Cloud and Zack were treated with JENOVA infusions by Gast, and as a result, their memories were intertwined with one another. Though Zack showed no ill-effects of the experiment, Cloud was violently affected. Zack eventually freed himself and Cloud, only to be killed by Shinra while he was trying to tend to Cloud's injuries. Cloud later on takes on Zack's Buster Sword as his own, believing Zack's memories to be his own.
Sephiroth however, did not die. His physical body lay damaged by the Northern Crater, but his willpower and mind kept his psyche alive. He is able to astrally project himself into different places, and can even create clones of himself, to further his plans of taking black materia. With this materia, he can call down Meteor. However, Holy materia can stop Meteor, and he wanted to make sure that no one can call down the Holy.
During the events of FF7, Sephiroth appears to Cloud frequently as a voice in his head, taunting him at times. This is because the JENOVA cells that had been injected into Cloud allowed Sephiroth some measure of control over Cloud's body, admitting in fact that Cloud was nothing more than his puppet. Sephiroth also kills Aeris Gainsborough, the half-Cetra, before she can call down Holy and stop him from calling on Meteor. The Sephiroth who kills Aeris however, is only one of his clones; Sephiroth can only project himself mentally instead of physically, given his damaged body, so it is he who controls all the clones, and to a certain degree, Cloud. He is able to control Cloud into giving him the Black Materia, and he summons all his other clones to the Northern Crater to prepare to call Meteor. This is Hojo's Reunion theory, where he hypothesized that all JENOVA cells call to each other, and would eventually be drawn to one place where they will meet, which is in the Northern Crater. his was one of the reasons why he injected his subjects with JENOVA cells and started the Sephiroth Copy project - to see if the theory could be proven.
However, Aeris' prayer for Holy seemed to have worked, and after venturing into the Northern Crater themselves, Cloud and his party are able to defeat Sephiroth. As a last ditched effort, Sephiroth mentally calls to Cloud in his mind to fight him astrally one last time, but Cloud's own will had grown stronger than the last time he had been controlled, and he was able to kill Sephiroth for good.
The sad thing was, Sephiroth was not actually a manufactured SOLDIER born of JENOVA, as he had believed himself to be. JENOVA, thought by Shinra to be an Ancient / Cetra, was actually the alien who battled with the Cetra and was imprisoned in the geological stratum. With the exception of the JENOVA cells being injected into him in his mother's womb, Sephiroth had a normal biological conception. Had he known this, he would have never gone mad and tried to rid the world of those he thought killed off his race, the Cetra.