There are a number of reasons for this. Let us look at a few of them.
First, it may be that many countries are turning to such a form of government because that is what their people want. People like to have freedom. Democracy is the form of government that gives the most possible freedom.
Second, it may be that many countries are turning to democracy because there is no other viable choice. It is clear that communism is not a feasible form of government. Therefore, with almost all of the most important countries in the world having some form of democracy, democracy is the most sensible thing to try.
Finally, it may be that they are turning to democracy because they want to emulate the success of countries like the US, Australia, Japan, and many others. They want to be like those countries because those are the countries that are successful. This trend may be pushed along by those countries’ policies of trying to promote democracy as well.