American GSM networks use 1900MHz. The rest of the world uses 900 and 1800MHz. A phone that can function in all three is a tri-band.

Some earlier GSM 'world phones' (such as the T28W and most Nokias) work in 900 and 1900MHz, meaning they work fine most of the time when outside of America.

However non-US operators' use of 900 and 1800 can mean:
- only 900 (older networks)
- only 1800 (newer, not-so-rich networks such as Bouygues in France)
- both 900 and 1800, with partial or full overlap in coverage.

Thus a tri-band phone will give you a higher probability of getting a connection when the 900 cells are busy, and when your operator of choice has no 900 coverage in the area (I use Bouygues in France when available as they have cheaper roaming charges).

Do get a tri-band if you can. The new higher-end Ericssons (T39m, T68) really have all the features you may need. Build quality seems a slight step down from the T28, which was exceptional in that regard.
The Motorola Timeport tri-bands are fine too, if a little bulkier.