He defeated one of the largest militaries in the world and was president during the fall of the ussr. Wouldn’t these things make him very popular among the people?
I've written about related topics before so I'll adapt some of that answer here. Bush did in fact enjoy very high approval ratings following the Gulf War. A lot Democrats were afraid to enter the race early on because common wisdom held it was a losing battle. SNL ran a skit in November 1991 called Campaign '92: The Race to Avoid Being the Guy Who Loses to Bush. Clinton isn't even featured as a potential candidate, showing how much things changed over the next year.
Once Clinton entered he faced questions from the press about his political experience, his extramarital affairs and more. But at the same time, he carefully crafted a campaign that avoided talking much about the war and focused on a soft spot for Bush, his domestic record. He accused Bush of being indifferent to high healthcare costs, of cutting important economic programs, and placed blame on him for the rise in unemployment.
Another important factor in the race was the presence of third-party candidate Ross Perot. Perot jumped on the bandwagon criticizing Bush's economic record, calling it "political voodoo" (appropriating a term Bush had once used against Regan). Perot was a self-made multimillionaire who disagreed with the Gulf War and was critical of free trade. In this way he tapped into some discontent held by a faction of Republican party which viewed wars and international treaties with skepticism. Pat Buchanan, for example, had challenged Bush from the right in the primaries. He called himself a "nationalist" and criticized the Republican establishment for the war and the tax increase and generally painted the modern party as soulless and opportunistic.
As Bush's popularity boost from the war waned, he proved helpless against attacks from both the right and left over the 1990 tax bill. He had worked with Democrats in congress to push through a tax increase, breaking his promise to "read my lips, no new taxes." But by late 1991 the unemployment rate continued to climb and there was a feeling that both parties had little ability to do anything about the economy. As late as June 1992 Perot actually lead the field in some polls, a sign of how little trust the public had in the establishment.
Bush also proved unable to shake the fallout of certain perceived gaffes along the way. In one incident at a campaign stop at a grocery store, he was reportedly "amazed" by barcode scanning technology that had been in regular use for a decade, reinforcing the stereotype that he was an out-of-touch, wealthy elite. Later reporting questioned the story's accuracy, but the fact that the narrative took off gives some insight into how the public viewed him.
In the aftermath of the violence following the 1992 Rodney King verdict, Clinton arrived in LA before Bush and, without directly blaming his opponent, turned it into a political win by claiming the country needed a president who could "reunify" the people. Meanwhile Bush got hammered in the press for his handling of the crisis.
In the end, Clinton eked out a victory by smooth-talking his way around his controversies and creating a coalition of centrists and left-leaning liberals along with 83% of the black vote. This was enough for 43% of the popular vote and, thanks to the presence of Perot on the ballot, an electoral college win.
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