Whenever we are trying to explain what happened in something as complex as the US economy and the federal budget, there will be many factors that could be involved. Different people will place different levels of importance on the various factors. This is particularly true when, as in this case, politics are involved.
Some people give President Clinton the credit for the change you mention. They point out that he raised taxes and decreased the level of government spending (when measured as a percentage of gross domestic product). They argue that these actions allowed the federal deficit to be erased and turned into a surplus and they wonder why Republicans today insist that tax hikes are harmful.
Others argue that Clinton was largely lucky and was only partly responsible for any of the growth. They argue that Clinton’s spending cuts (and those initiated by President Bush before him) showed the business community that the government was going to act responsibly. The business community was therefore more confident and was willing to take risks that ended up making the economy grow. As the economy grew, tax revenues increased and less money had to be spent on things like helping the poor.
There are also those who say that the technology boom/bubble helped to inflate a bubble in the late 1990s. They say that Clinton was just lucky because he happened to be president when people were getting so excited about these new technologies (like the internet and personal computers). This excitement fueled spending in the short term and allowed the economy to grow.
Many factors, then, helped to erase the deficits of 1992. Ultimately, however, the proximate cause was that the government started to take in more money and to spend less.