A GSM phone that supports three of the four major GSM frequency bands, and will therefore work in most parts of the world.
Of the four major GSM frequency bands, 850 and 1900 are the two bands used in North America. 900 and 1800 are the most common bands in other parts of the world.
There are two major types of tri-band GSM phones: European and Americas.
European tri-band phones support the 900, 1800, and 1900 frequency bands. Therefore they provide complete coverage in Europe, Africa, and Asia, and work on at least one network in most countries in the Americas.
Americas tri-band phones support the 800/850, 1800, and 1900 frequency bands. They provide complete coverage in the Americas, and will work on at least one network in most countries in Europe, Africa, and Asia.
Tri-band is not be confused with tri-mode. Tri-mode usually refers to a CDMA phone, while tri-band usually refers to GSM phones.