Dual-band - definition
Mobile phone networks work using signals on specific frequency bands and a phone must support those bands in order to work with the network. Dual-band refers to the phones ability to work with two different bands. It is important to specify which bands exactly.
Networks in different geographical locations work on different bands - GSM networks in the Americas use the 850 MHz and 1900 MHz bands while networks in Europe, Brazil, Asia and Africa use the 900/1800 MHz bands.
For example an 900/1800 dual-band phone won't work in the US and an 850/1900 phone won't work in Europe. A 900/1900 phone should work on at least one network in most countries around the world.