There are two plausible explanations, one of which seems to have a little more oomph than the other. Peter A.G. van Bergeijk has argued that some of the explanation is likely to have occurred from inadequacies in the IMF statistical system. As he points out, in a conceptual sense any exports from one country must be imports to another country--so the official statistics gathered by each country should add up in a way that global exports are equal to global imports. However, when the IMF adds up it statistics, it finds that total world exports exceed total world imports by $206 billion. This factor alone isn't sufficient to explain a $3.7 trillion drop in global GDP, but it does suggest that there are some problems in the underlying statistics.
For one vivid example, the GDP of Russia was $1,861 billion in 2014, as measured by converting Russia's GDP measured in rubles to US dollars at the 2014 exchange rate. However, the US dollar increased a whopping 57% against the Russian ruble in 2015. So when take the GDP of Russia in 2015 as measured in rubles, and convert it into US dollars using the very different 2015 exchange rate, Russia's GDP in 2015 was $1,236 billion--down about one-third. Obviously, this decline in Russia's GDP isn't mostly about any change in goods and services produced in Russia's economy. It's about using a different exchange rate for converting between rubles and US dollars.
Indeed, if you look at the very bottom row of Table A1 in the October 2015 issue of the World Economic Outlook, you see an estimate of world GDP that is based on "purchasing power parity" exchange rates, which are exchange rates calculate by the International Comparison Program at the World Bank. The idea is to look at what a currency can actually buy--that is, its "purchasing power"--and to calculate what exchange rate would lead to equal purchasing power of currency. Exchange rates are much more volatile than prices of goods and services (like the 13% rise in the US dollar vs currencies in the rest of the world in 2015, or the 57% rise in the US dollar vs. the Russian ruble). Thus, when PPP exchange rates are used to convert GDP to US dollars, the result doesn't leap up and down with market exchange rates. Using PPP exchange rates, world GDP increased from 2014 to 2015 from $108.7 trillion to $113.1 trillion. (Those who want some additional discussion of purchasing power parity exchange rates might begin here.)
This explanation addresses the specific issue in IMF statistics about world GDP from 2014 to 2015, but it's important to remember that there's a bigger issue here. Intro textbooks explain that one of the uses of money is as a "yardstick" so that we can compare values of goods and services and work and saving using a single measure. The difference between market-value exchange rates and purchasing power parity exchange rates is an especially vivid example of how the yardstick of can be misleading.
But it's also true that the process for calculating the PPP exchange rate is a difficult one, full of underlying assumptions. In 2010, recent Nobel laureate Angus Deaton devoted his Presidential Address to the American Economic Association (freely available on-line here) to detailing the "weak theoretical and empirical foundations" of such measurements. When the PPP exchange rates are recalculated and readjusted every few years, the changes are often quite large--which confirms that the PPP calculations should be treated as having a substantial margin of error. For purposes of comparing world GDP from one year to the next, the PPP exchange rate is probably more accurate than the market exchange rate--but there's no reason to think that the PPP exchange rate is exactly right, either.
Domestically, we typically refer to US output as measured in money terms of US dollars, but a national-level GDP statistic doesn't take into account regional differences, like how higher oil prices are a positive for oil-producing regions but not for others, or how housing prices can vary substantially between states and between urban and rural areas. Measurements based on the common yardstick of money is a shortcut that is often useful and productive. But of course, what ultimately matters for people is not value as expressed in money terms, but rather the quantities of goods and services that can be consumed, along with hours worked.