There are at least two types of tri band phones, and quad band phones. All would be considered world phones, but not all would work in all parts of the world.
The four frequencies are 850, 900, 1800, 1900
850 and 1900 are used in the united states
900 and 1800 are used internationally
See this page for country specific information
http://www.gsmworld.com/roaming/gsminfo/index.shtml
When you get a GSM phone in most places in the United States it has a SIM lock turned on. Because the wireless companies heavily discount the phones, they lock them so you can only use them on their service. To take that phone and put another SIM into it to use in another country without roaming, you need to get the phone unlocked, or get another unlocked phone. Unlocked tri bands can be had for as low as $60 or 70.
Don't go by the designation world phone, that may or may not mean anything. It could be a single band phone that doesn't work here in the United states, you may not want that.