The GSM standard originated in Europe, where mobile phones occupy two frequency bands: one in the 900 MHz range and one in the 1800 MHz range. When GSM technology crossed the Atlantic to the Americas, it was impossible to reuse the same European frequency bands since those had already been allocated to other devices by the FCC. Hence, a different pair of frequency bands were made available for GSM use: the 850 and 1900 MHz bands.

In summary, a quad-band mobile phone is used to designate a phone that can operate in the following GSM frequency bands:

850 MHz (U.S.)
900 MHz (Europe/Asia (ex Japan and S. Korea))
1800 MHz (Europe)
1900 MHz (U.S.)
Some companies refer to this feature as "World Phone", due to the variety of bands a quad-band phone supports.

Note that hardly any quad band phones cover GSM 400 (450 - 480 MHz), a band used in sparsely populated areas or in less developed countries due to its longer range. While a "quint band" phone (400/850/900/1800/1900) is possible none has yet been announced.