"Typhoon" is the regional name for a tropical cyclone with sustained surface winds over 33 meters per second (74 miles per hour) in the northwestern Pacific Ocean west of the International Date Line all the way to the Asian mainland coast; the same storm would be called a hurricane if it were in the Atlantic Ocean, the eastern Pacific, or the south Pacific east of longitude 160 east (just west of New Zealand according to a BBC map). The map shows the Philippines in the zone that has typhoons, but Indonesia and New Guinea are in an area where the same type of weather is called a "severe cyclonic storm." The World Meteorology Organization in Switzerland are the people who officially decided the borders for the usage of each regional name.
A.Word.A.Day says that the word is originally "from Cantonese toi fung, from Mandarin tai (great) + feng (wind) by
influence of other terms (Greek typhon, Arabic/Urdu/Hindi tufan, et al.)" Many other sources agree with Webster 1913 that the Greek "typhon" was the true source, saying that "touffon" and "tufan" appeared in English via the Arabic/Hindi borrowing, meaning a storm in India, as early as 1588; while the Cantonese (spelled by the American Heritage Dictionary as "Taaîfung") does not appear in English until 1699 as "tuffoon." (I don't have nearly enough linguistic expertise to see how they can say one of those comes only from the Greek but the other only from the Cantonese, myself.) The modern spelling, influenced by both words, first appears in 1819, in Shelley's Prometheus Unbound.
Sources:
http://news.bbc.co.uk/1/hi/world/202344.stm
http://www.aoml.noaa.gov/hrd/tcfaq/A1.html
http://www.bom.gov.au/bmrc/pubs/tcguide/globa_guide_intro.htm
http://wordsmith.org/awad/archives/0903
http://dictionary.reference.com/search?q=typhoon