Why did Bobby Fischer play the 1992 rematch with Spassky? As title above, why did Bobby Fischer play the 1992 rematch with Spassky after some 20 years of inactivity? Was it because he was in need of money? Or was it, as Fischer explained in the press conference, because it was the first offer to play at his conditions? Or are there other actual reasons for his unexpected comeback?
After beating Spassky in 1972, Fischer laid out terms that were deemed unreasonable for his title defense in the next world championship against Karpov. With no resolution, Fischer's title was forfeited and Karpov became the new WC by default. Fischer subsequently fades into obscurity.

Nevertheless, Fischer never accepted his title loss, and still considered himself to be the WC, having never actually lost a WC match. Thus, for what he considered to be his title defense, he plays a rematch against Spassky in 1992, with a prize fund of US$5 million.

Fischer wins the rematch, declares himself the undisputed world chess champion (a claim that isn't widely acknowledged, with Kasparov as the official reigning champion at the time), never plays competitively again, and the rest is history.

To explicitly answer your question: Fischer was trying to assert that he was the world champion, contrary to the official result that he had already lost his title in 1975. He also needed the money, which may or may not have been the more  significant factor.


  Source: Kasparov, Garry K. The New York Review of Books, Volume 58, Number 4 - The Bobby Fischer Defense. 10 Mar. 2011
  
  
    It was therefore quite a shock to see the real live Bobby Fischer reappear in 1992, followed by the first Fischer chess game in twenty years, followed by twenty-nine more. Lured out of self-imposed isolation by a chance to face his old rival Spassky on the twentieth anniversary of their world championship match—and by a $5 million prize fund—a heavy and bearded Fischer appeared before the world in a resort in Yugoslavia, a nation in the process of being bloodily torn apart.
    
    [...] Fischer, who still called himself the world champion [...]