Globish, derived from global + English, is the term used by Jean-Paul Nerrière, a former vice-president of IBM, for a simplified version of English that he is promoting for international communication.
Mr Nerrière's Globish uses a list of 1,500 words (available here in a pdf) and suggests that with this reduced list people will be able to communicate. His basic aim is fine; international communication doesn't need native-speaker competence and avoiding humour and idioms is a regular part of training in many companies for English speakers to help them communicate with non-native speakers. There's some software too that identifies words that aren't on the list to enable people to write more clearly.
However, the list is weak. Are slave and dictator really more important terms in modern international communication than contract? The choices he has made seem far too arbitrary for this list to be very successful. You will be fine in a wine and cheese party as a Globish speaker, but will find it hard to order chicken or buy a beer. Computer is in, but the internet and website are out; words that are very international are not in, but are these both so international? He wants companies to train their staff and adopt it, but the word list that is the basis of Globish is all over the place- we have wage, but not salary, etc. It is far from clear what the criteria were for inclusion in the list. The Glolexis software to go with Globish will offer synonyms, so it could tell me to replace beef with meat of cow, but I would love to know what it would do with chicken. I see it as rather dogmatic and unlikely to have much impact on the development of international English. In Globish, different forms of a word are seen as legitimate extensions of a base word; an example given is care, giving us careful, carefully, carefulness, careless, carelessly, carelessness, uncaring, etc. This raises the question of why we have both chemistry and chemical in the list; one of them would have been enough.
A number of newspapers have reported on Mr Nerrière's Globish, but I expect that, like so many other attempts to reform English, it will disappear soon enough. International demands for efficient communication across cultures are going to have a huge impact on the language and a simple level of English is very useful, but so much of our communication is at a very advanced level and requires far more subtlety than this method would allow.
The term Globish is also being used by MN Gocate, who is advocating a spelling reform.