Globish = global + English
Globish was apparently coined in 2007 by French-speaking retired IBM executive Jean-Paul Nerriere. He noticed that a sort of "decaffeinated English" was becoming the lingua franca of international business and politics. It's "decaffeinated" because non-English-speakers have assembled only enough of an understanding of English to use it to communicate with other non-English-speakers, though it isn't as rich as British and American English are.
He noticed in Japan that non-English-speakers were communicating more effectively with other non-English-speakers than with the Americans or the British, even though they (the non-English-speakers) were using a subset of the English language to communicate. Nerriere dubbed this new means of communication Globish.
Robert McCrum will soon be publishing a book called Globish: How the English Language Became the World's Language, which details Nerriere's story and goes into further depth about how English is spreading throughout the world. You can read more about it in his blog post, which also features this wonderful photo that seems to define irony: