"Centrino" is a brand name that incorporates the use of specific hardware. Namely a Pentium M CPU along with the use of certain chipsets and certain wireless network cards. The specific combinations of hardware are "Centrino certified" to get the best mix of performance, mobility, battery life, and connectivity.
A Centrino setup can be used for gaming if it's paired with a decent video card. I'm typing this on a Centrino based laptop right now with a 1.86GHz/2MB Cache Pentium M and 2x512MB DDR2-533. This laptop just has the i915G graphics controller but a better video card would certainly have me playing some of the newer games on the market.
As for the wireless from city to city, that all depends on what sort of WiFi they have setup and what you pay to access it. Some of the mobile phone companies such as Verizon offer mobile broadband but I haven't tried any of them so I don't know how reliable or fast they are. There are coming technologies, such as WiMax, that are aimed at bringing wireless broadband into areas that are currently limited to dialup connectivity...they may also address the "always connected" issue.
More about Centrino here:
http://www.intel.com/centrino/
This post has been edited by nmX.Memnoch: 18 December 2005 - 12:35 AM