If you're talking about magical powers, then that would be materia, just like everybody else in the game, though after he falls into the lifestream during the nibelheim incident, it's never confirmed whether or not he actually needs materia to cast the less unique spells (i.e. he still needs materia to cast meteor, but nothing else can be confirmed) although when cloud hands it over in the northern crater it does appear as though sephiroth absorbs the black materia, so he may have done this with other materia also. Other powers such as telekinesis are from an unknown source, but may either be from his higher than normal concentration of jenova cells or a materia unavailable to the party.
Sephiroth's physical power comes from what is mostly the same procedure as everybody else accepted into SOLDIER. However, sephiroth, unlike the others, was injected with jenova cells while he was still inside the womb, meaning they are a far more important part of his DNA, and making him much stronger than any of the other SOLDIERs. It is also believed that he underwent many more mako treatments (or showers, as they are sometimes referred to) than is normal, which may account for some of his increased power, though it is largely accepted that the jenova cells being injected before birth is the main reason for this, as he is still more powerful than cloud, who was immersed in mako for years. His skill as a warrior comes mainly from the fact that he has never known anything else. Lucrecia tells us in the crystal cave that she never once even got to hold sephiroth. he was taken by shinra at birth and raised to be the ultimate SOLDIER. It was because of his success that the organisation was even born, though it was considered to be ineffective to have to raise from birth and find willing mothers each time, and so the injections of jenova cells and mako were done after the subjects were fully grown, reducing the efficiency. Thus why Sephiroth is the greatest SOLDIER.