Sephi (as the fangirls, and some fanboys refer to him) was the product of the jenova project. Which was headed up by Prof Hojo, who is also Sephiroth's pops, and prof Lucretia, his birth mom. Now Hojo and Lucretia, whome was the object of Vincent Valentines affection (but that's niether here nor there so lets move on), were a couple of scientist who had a thing on the side. So when Lucretia got knocked up Hojo decided it would be the perfect opportunity to further the experiment, and so he injected JENOVA cells into the fetus.
Well long story short Sephiroth was born, Lucretia was thought to have perished during labor, and Hojo shot Vincent and turned him into a guinea pig.
Fast forward twenty something years, Seph's a rising star in SOLDIER. The hero of the great war with wutai, and probably getting more tail than the Rolling Stones (er probably not as much as the stones, but pretty close). As mentioned above he had two best friends, both of whome were the results of a similar project, project Gillian. Lots of stuff happened one of his buds dies, at the hands of Zack Fair (Clouds buddy, Aeris beau). The other one's more complicated to explain, but you can thank him for making Sephiroth the town burning, meteor summoning, flower girl killing, badass he becomes.
Well during a routine mission to the Nibelheim mako reactor (not that routine if your sending two members of SOLDIER to investigate instead of reactor speacialists), Sephiroth had a sudden case of the crazies. You see Sephiroth, Zack, Cloud (who was just an infantryman at this point) and their guide Tifa were investigating strange goings on at the old reactor. (Sadly unlike that episode of scooby-doo it did not turn out to be the grounds keeper old man Jenkins.) Amazingly this reactor, out of all the other reactors in the world, held the secret to Sephiroth's origins as a lab experiment.
While conducting a thorough search Zack and Sephiroth stumbled upon a room deep within the reactor. Within this room were the failed "sephiroth" clones created by shinra. (Apparently you can't succesfully mass produce super soldiers in any universe, eh live and learn I guess.) Que Genesis emerging from the shadows to make this fact abundantly clear to Seph, who had realized they were experiments but not based on him. In this room Sephiroth also found a door with the name Jenova written on it, he having been told all his life that his mothers name was Jenova (so it wasn't such a strech for him to connect the dots), these revelations led to him locking himself in the basement of the Shinra mansion.
One all-night cram session later, Sephiroth demolishes nibelheim. Slaughtering almost everyone and burning it to the ground, then heading off to the reactor to see his mum. Zack, Tifa, and Cloud (who arives after the other two) all confront Sephiroth. Tifa and Zack both get their asses handed to them, but Cloud feuled by righteous rage (and cause he's the hero of the story, and maybe cause Seph's attention is mainly on Jenova, as he's finally face to face with his "mother") manages to stab Sephiroth with Zacks buster sword. Thinking Seph's done for, Cloud goes back to tend to his friends. Meanwhile Seph decapitates Jenova and begins to make his way out of the reactor. Cloud tries to stop Seph again, but ends up getting stabbed instead. But since he is the hero of the story and still full of that "you destroyed my hometown" anger, he summons amazing strength and lifts Seph up by the sword (which is still inserted firmly in his chest) and launches him off the catwalk into the lifestream that runs beneath the mako reactor. Well Cloud passes out and we don't hear from Seph until Four years later.
Well that went by quick, four years later Cloud and Zack escape from a rebuilt Nibelheim. Zack gets capped just outside Midgar, so Cloud has to do the living for the both of'em. Long story short he teams up with AVALANCHE, or badass greenpeace as I like to call it. Avalance consists of (B.A. Baracus look'a'like) Barret, Tifa (how can she find a shirt to fit over those) Rockheart and three redshirts who die. Later they meet Aeris the flower girl, and stuff happens that has nothing to do with Sephiroth. Well until a daring rescue attempt that leads our stalwart group into the Shinra building, and getting locked up.
Well turns out Jenova's body, sans head, was brought there for safe keeping. Sephiroth whose been traveling the lifestream for the past four years has learned a lot of new tricks, including imposing his will on any part of Jenova's body and controlling it from afar. Changing her body into a copy of himself Seph proceeds to repeat what happened at nibelheim, by cutting a swath of death and destruction through the upper floors of the shinra building.
To make a long story short Cloud and his group travel the world trying to stop Sephiroth's evil plan. Which would appear to be world domination or destruction. Well Seph summons meteor, kills Aeris, and just becomes an all around nuisance. Sealing himself in the northern crater, were he had been the whole time crytalized in materia. The heroes meanwhile have to deal with sidequests and the WEAPONS created by the planet, that were unleashed when Seph summoned meteor and sealed himself away. His real plan being to become a god by crashing meteor into the planet forcing the planet to gather lifestream energy at the wound in order to heal itself, he would be at ground zero to absorb the lifestream into himself and become a god.
Finally they proceed to the crater and face off against Seph. First encountering Bizzaro Sephiroth, a monstrous mishapen version of Sephiroth. Defeating him Seph transforms into saefer Sephiroth, closely resembling an angel. Defeating him, cloud faces a shirtless sephiroth one last time in the lifestream, and completely pwns his ass with omnislash. An so Sephiroth dissolves into the lifestream his plans for godhood undone and his legacy as badass cemented.
This is the day you shall always remember as the day that you almost caught Sephiroth.