Quad-Band Designates a GSM phone that supports all four major GSM frequency bands, making it compatible with all major GSM networks worldwide. The famous iPhone is a quadband phone. 
The four bands include the 850 and 1900 MHz bands - used in the Americas - and 900 / 1800, used in most other parts of the world. Compared to a tri-band phone supporting the 900 / 1800 / 1900 bands, a quad-band phone adds support for GSM 850 for full coverage in the Americas. Compared to a tri-band phone supporting the 850 / 1800 / 1900 bands, a quad-band phone adds support for GSM 900 for full coverage in Europe and Asia.