Q. How does the Chrome browser know where I am geographically when I see my city listed on the side of the Google search page?
Google's Chrome, like other browsers, uses network information from the computer to figure out your approximate location and then matches it up in a location database. This information can include the nearby Wi-Fi network routers (including the one you are using) and their signal strength, as well as your computer's Internet Protocol (I.P.) address. (Google often used the cars that took picture for Street View maps to collect information on Wi-Fi's. )
Some Web sites may also ask to use your location information for the purpose of showing you local listings and advertisements, but you can opt out. Google has an explanation of location sharing in the Chrome Help pages on its site.