Gast and Hojo's Jenova Project (the full story of which is here) involved infusing worthy subjects with cells extracted from Jenova's body, which was found in a 2000-year-old geological stratum. Every member of SOLDIER - and, of course, all the "rejects" who weren't strong enough to become members of SOLDIER - had Jenova cells inside them. These Jenova cells, combined with the exposure to large amounts of Mako energy, were what made them so strong.

However: at a certain time, all these subjects would feel something calling to them to come together at the Northern Crater. This was Jenova calling, because she was still very much alive in the Lifestream and the Northern Crater and wanted to bring all her cells back together. This seems fair enough to me - if your body has been split up into little bits and your cells have been implanted without your permission into people you've never even heard of, it's understandable that you'd be a little grouchy.

Anyway. Gast and Hojo had released parts of Jenova by taking her cells to be injected into the Jenova Project subjects: this meant that she could excercise control over these subjects, or "puppet" them. It was this that called every Jenova-infused individual - including Cloud - to return to the Northern Crater so all of Jenova's cells would be together again. (Hence the name "reunion".) Therefore, Jenova would be reincarnated and would be able to continue her quest to take over the world. The Reunion itself takes place just after the Whirlwind Maze, in disc two of the game.

Jenova's only line of dialogue in the whole game is about the Reunion. While it is not spoken when the party are anywhere near the Whirlwind Maze or the Reunion itself (she says it after Sephiroth kills Aeris in the Forgotten City and the party fight Jenova*Life) it still refers to it: the line she says is, "...because you are a puppet" - referring to the fact that Cloud is a specimen of the Jenova Project and that Jenova is able to control him as her "puppet".

Incidentally, the third form of Jenova - Jenova*DEATH - is fought when Cloud and the rest of the party reach the Whirlwind Maze on the way to the Reunion. For more information on the four Jenova battles, take a look at the battles page.