How is my iPod Touch able to determine my location when I'm offline?

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.

Before you leave for your trip you'll need to install an offline mapping app like "CityMaps2Go". You need offline maps because you will not actually be connecting to the internet while you are doing your sightseeing.

When you arrive in a new city you'll have to find a hotpot (hotel, Mcdonalds, Starbucks etc) and connect to the internet. This is the one and only time you need an internet connection.

Open either the built-in Apple "Map" app, or the Google Maps app, and open-up the "directions" option. Now enter any two points in the city, like from the train station to your hotel, or between any other two points of interest.

After the app gives you directions the device will automatically load a database (from Apple) of all Wifi hotpots in the entire city! That database will now reside in the memory of the iPod Touch even after you exit Google Maps, and until you reboot the device. Any other app that uses the location service can now access that database.

At this point you no longer need to be connected to the internet, but the device must still be in Wifi mode. As you are walking around the city the device will be detecting Wifi hotpots (but not connecting to them), the device reads the hotpot's MAC serial number and in the background looks up the hotspot's coordinates off the database, and is able to determine and show your exact location anywhere you are in the city with an offline map app like CityMaps2Go.

I've now used this feature successfully in Budapest, London, the Big Apple, Toronto, Amsterdam, Beijing and Hamburg. It's very accurate, determines your location in milliseconds, and I haven't come across in gaps in coverage.