Wealth and availability
First of all, where did this statistic come from?
Secondly, do you want to know why Americans take more drugs, or why there is more availability of drugs here than in other countries?
The problem with a question like this one is that it's too broad and is generally used (it may not be the case here), to point out the Big Bad USA taking the world's resources, or being in need of so many drugs (as if the US population is miserable, sick, dying, or just really screwed up). This question is similar to "Why does the US use a greater percentage of the world's energy even though it doesn't have the greatest percentage of US population?" No one is actually looking for an answer, they just want to play the Big Bad USA game. The simple answer to that one is: The USA is the most industrious, most productive, is a first world country, and is the world super power. Of course it uses the most energy.
If you're really curious as to why the US holds 75% of the prescription drug market, then I'll try to venture a guess.
I am by no means an expert on prescription drugs, so this is just a guess. It is no secret that the United States is the most wealthy country in the world and prescription drugs cost a lot of money. That's the simplest way I can answer one take on this question.
If you're asking why do Americans take more prescription drugs than in other countries, then I can only guess again. To answer more specifically, I'd need a breakdown of what kinds of drugs are being sold, and what percentage of those drugs take up the market. What percentage are for physical illness, infections (antibiotics), dysfunctions, anti-depressants, birth control, pain, etc.
Because America is so wealthy, we can afford to take drugs for whatever "problem" we have, whereas in other poorer countries they cannot afford to have the more selective medications. But for other first world countries, like some European countries or Japan, I think you'd have to start looking at the culture. How often do they work, what is their environment like, etc. Also examine the soundness of the government. If we look at all the countries in the world, that means you need to include the Congo, Uganda, Iran, Syria, the former soviet satellite states, Mexico, etc. etc. all of which have corrupt governments.
To make this post not so long: depending on what angle(s) to this question your taking, it would take an entire book to answer the question to satisfaction.
The short version probably is what I wrote up top: America is the wealthist nation and can afford the drugs.