How is my iPod Touch able to determine my location when I'm offline? When I'm traveling through a city, as long as there are wifi networks nearby (even if they are secured with a password), my iPod Touch can determine my current location with great accuracy—obviously not as well as a GPS can in the iPhone, but still very well.

How is it able to do this exactly? Could someone explain the technical side of this, or does anyone actually know how this works?
Apple uses WiFi hotspots (and presumably the corresponding signal strength) to triangulate your position using a data from Apple.  Similar to how Google maps a hotspot using their StreetView cars, a 3rd party at one time scanned the area you travelled to and mapped the SSID and probably MAC address of the local hotspots.

Though I don't know if they still do, Apple at one time did not maintain this information internally but sourced it from a 3rd party.  Some of the initial privacy concerns about iOS regarded how this information was 'phoned home' to Apple without consent;  That is, when your iPod was connected and 'knew' its location, it would also scan the local SSIDs and send them to Apple to improve/update the database.

This data was sourced by Skyhook Wireless.

Based on my own inference from experience (though not 100% sure, and I no longer use an iPod, so even if this was true at one time it may not anymore be so), when you map a route in Maps, it caches the relevant SSID information for the areas to which you are travelling before it goes offline.