Wi-Fi is the very same sireless entowrk as one would find on a laptop. Either 802.11b or g. That cell phone has to be within a wireless netowrk range in order to work, just like that of a laptop.
'Quad-Band' refers to the GSM network of 850/900/1800/1900 Mhz. AT&T uses the 850/1900 and T-Mobile has the 1900 primarily and 'roams' on AT&T's 850. The rest of the world uses the 900/1800/1900 bands. Now this would mean on a quad-band cell is that it can be used on any 'gsm' netowrk around the world....provided you have a international plan with either AT&T/T-Mobile, or have a GSM sim card from the local cell provider for that country.
Important side note, if you are using a 'Tri-Band' that usually referes to 900/1800/1900, you won't be able to connect to an area where AT&T 850 Mhz is not available. And AT&T does not 'roam' on T-Mobile's 1900 Mhz.
Verizon and Sprint uses CDMA/iDEN networks which is incompatible with GSM networks.
Hope that this answers your question.
what is wi-fi technology on phones? what does it do?... also what is quad-band?