There are a multitude of reasons why this is true but I can give you a few quick examples.
The military power of the British Empire initially helped spread the language across the world. The economic power of both the British and the Americans further solidified this.
Huge advancements in technology have allowed American movies, music, press, radio, etc. to be broadcast and consumed the world over.
The rise of multinational corporations with presence in multiple countries helped facilitate a "common" language to adhere to. These companies also greatly increased language visibility through aggressive advertising.
Most of the 20th century was ruled by American economic supremacy, solidifying English as the de facto language for commerce.
The VAST majority of scientific papers are published in English. Over 80% of the everything on the internet is in English. If you want to be competitive in sciences and technology, you need to know English. With the advent of the internet, a scientist in India can easily speak to one in Austria who can speak to his colleague in Boston. This loses a great deal of practicality if there is a language barrier between them.
Ultimately, English was in the right place at the right time. By the beginning of the 19th century, Britain was the worlds leading industrial and economic powerhouse. They were usurped only by another, larger English speaking nation. So for the last 200+ years the world power has been an English-speaking one, and these years have seen the fastest advancement of human technology ever. With the exportation of these new technologies and ideas a lingua franca was born.
Sorry for any grey areas, doing this on mobile
source: Daniel Spichtinger "The Spread of English"
If the internet and globalization had struck in the 17th or 18th centuries we would all be speaking and writing in French (as diplomacy, philosophy and vernacular science was done then); spanish in the 16 and 15th centuries, latin in the middle ages and roman times. English just happened to be the language of two successive dominant world superpowers for the past 150 years and has become the lingua franca, replacing french.