My flatmate and I have been trying to figure it out, and we guessed it had something to do with the British Empire and how the English language was spread around the world, but we're not entirely sure because of the spread of other large empires around a similar time.
There are really two distinct phases of the spread of English. The first is of course, the British Empire and her offshoots. This first phase was important, in that it spread English to more people and territory than any such spread since the Spanish Empire, but there is an important caveat to this expansion: it was limited in scope. By this I mean that English, despite being used as the language of administration and government in more places than anywhere else in the world, those who were actually governed were not necessarily learning English to that heavy a degree. Learning English was a pre-requisite for local elites, such as in India, to gain access to the levers of power in lower level administrative posts, but the majority of the people being governed under this language were not speakers, and it wasn't until relatively late in the colonial period that the education systems set up by colonial authorities in most of these countries started to develop enough to get the language being spoken more widely. The primary reason it continues to be spoken in many of these countries as a second language stems from the fact that most former colonies are actually made up of a multitude of ethnicities and languages. Let's take Nigeria for example. Were you aware that there are literally hundreds of different languages and dialects in the country? Here's a list: http://www.onlinenigeria.com/languages/languages.asp Post-colonial governments often utilized the language of their former over-lords to facilitate governance and communication across ethnic divides.
But this doesn't explain it's current explosion. For that, we have to look for the second phase, the American phase. This has pretty much all begun since the Second World War, and accelerated since the fall of the Soviet Union. But in practice, the United States's influence has been such a dominant one in business, technology, and over-all global power that numerous facets of life began to really require English as a key component of success. Now, that said, it wasn't simply a matter of someone needing that language because they knew they'd have to deal with Americans in a professional or scientific setting. The biggest reason for it's spread has likely been driven by the same factors that led former colonies to utilize it as well. That is, mutual understanding between two other languages. The choice of English can be attributed to the influence of the United States due to all those other reasons, but the actual force propelling it's adoption is simply that it fills a need, and serves the most utility for that need. If you need a language that allows people to communicate, you are going to choose the language that has the largest global power behind it almost by default. It's not all that dissimilar from the reason that French became such a prolific language in Europe.
Source: 'History of the English Language' by Baugh and Cable
hi! FYI, you'll find some additional information on this topic in the FAQ (link on sidebar):