Info

Who is he??
We don't have a lot of informations about Sephiroth in Kingdom Hearts, expecially in the American and European version of the game. Additional informations are given in the "Final Mix" version.
I supopse that Sephiroth comes from the same world of Cloud and Aerith, but I'm not sure. However, he is the unbeaten champion of the Olympus Coliseum, known as the greatest swordman of ever. For some time his whereabouts have been unknown, but now he's suddenly returned, and nobody knows why.
He and Cloud have crossed paths before, and they still have a matter to settle. It seems that is for Sephiroth fault that Cloud can't have peace. Now they're searching for each others...

In Battle
Sephiroth is an optional boss, but you can fight him only after unlocking the Hades Cup, and after you rescued Kairi. If you talk to Filott�te in the Olympus Coliseum you'll see ???? right below the Hades Cup. After that, it will be called the Platinum Match.
He's a REALLY strong opponent:
Total HP: 1800
Attack Power: 46
Defence Power: 46
EXP Obtained: 18000

Scripts
I found on the web two different translations of the Showdown of Fate, the scene between Cloud and Sephiroth in the Final Mix version:

First Version:
(After Sora defeats Sephiroth in the Platinum Match for the first time, the following scene plays when he exits the Arena's antechamber.)
Night. Cloud, sword drawn, walks into the arena. He stops as he sees a black feather slowly drifting down to the ground. Still focussed on the feather, Cloud sees a shadow quickly appear behind it, and just as quickly two feet land softly on the shadow. He looks up to see Sephiroth.
The arch-enemies stare at each other.
Cloud: "So we meet at last."
Sephiroth: "I was searching for you too."
Cloud: "As long as you exist, I can't wake from this nightmare. You are my darkness."
Sephiroth (gesturing widely): "If that's so, I shall draw you into the darkness. Into the nightmare that forever deprives you of light, from which you can never awaken."
Cloud raises his sword. Sephiroth slowly reaches for his. The two flicker with electrical energy, Cloud red, Sephiroth blue, and the pent up force draws small pebbles upwards off the ground.
Suddenly they charge, and their swords clash violently as "One Winged Angel" begins to play in the background. Again and again they trade blows, with no sign of weakness on either side.
They separate and again Cloud charges, this time pushing Sephiroth back. But Sephiroth vanishes, leaving only feathers, reappearing above in the air. Sephiroth holds out his hand to Cloud, and Cloud immediately charges. As their swords again clash, everything fades to white.

Second Version:
After Sora defeats Sephiroth, he leaves Collesium, scene switches...
Cloud, goes into the Collesium Arena, wandering around, he feels that something from the Darkness is coming. Thus after a distance, he stop. A feather drop on the ground, lightly, A footstep, steps to ground. Sephiroth, had a little smile on his face... They stared at each other.
Cloud: "So we finally meet again..."
Sephiroth: "I was searching for you"
Cloud: "Although my existance is limited, I can still feel you in the depths of my own nightmare... The darkness that existed in front of my own eyes."
Sephiroth: "I was the one who invited you to the darkness. Taking away all the Light, realized that there is no path of yours but darkness that awaits for you."
Cloud draws his sword, Sephiroth does the same thing, they prepare to engage into the Showdown of Fate. As they were posing themselves, the earth shakes, tense of the atmosphere is too strong that the controller vibarates...
They then charge foward, Sword and sword clashed, and they move back, charges foward again, Cloud turn his body, and blocks Sephiroth's attack, thus they did a lot of consecutive attacks from the ground to the air. But they both drawed, Cloud flies foward to slash Sephiroth, but Sephiroth teleports away, into the higher air. Cloud looking up, and they both stared at each other again, and then they charges towards, and their swords clashes again, screen whites out.