Many phones are advertised as being "tri-mode" or "dual-band", etc. These refer to the combination of technologies and frequncy bands the phone supports.
AMPS is the analog technology, which has inferior features and quality, but often superior coverage. Digital technologies include CDMA, TDMA, and GSM.
The two frequency bands in the US are 800 MHz (Cellular) and 1900 MHz (PCS). Europe and many other parts of the world use 900 MHz and 1800 MHz. The 800 MHz band is also sometimes referred to as 850, specfically when referring to the new "GSM 850" mode.
As an example, a CDMA tri-mode phone would support AMPS 800, CDMA 800, and CDMA 1900. That means it would work in both frequency bands in digital, and also work in analog (which is only 800 MHz.) The same is true for TDMA.
A dual-mode CDMA phone could be either AMPS 800 / CDMA 1900, or AMPS 800 / CDMA 800. Same for TDMA.
GSM is the dominant standard in Europe and many other parts of the world, and so there are also dual-band and tri-band GSM "world" phones that support GSM 1900 and one or both of the European frequency bands.