On Android, the "Power saving" option within the location settings means that wifi and mobile networks are used to determine location. What data points from these access points does it use and how does it factor these into calculations?
Let's first assume that GNSS (GPS, Galileo, Glonass, BeiDou) were the only way to fix your position.
What Google is doing, is that your phone keeps a list of every WiFi and mobile phone base station it has ever seen, together with the signal strength, timestamp, and location of the phone, and periodically uploads this list to Google.
If, for example, there are three Android users in the vicinity of a particular WiFi base station, Google now knows the exact position of the three phones, and the signal strength which which each phone received that particular base station. Signal strength correlates with distance, which means Google can now trilaterate the exact position of that base station.
In reality, there will be much more than three Android users in the vicinity of a base station, and they will see much more than one base station (from where I am sitting right now, I see about 30).
In addition to that, it would also be possible to equip the vehicles used for Google StreetView with radio scanning devices to improve the location data in urban areas with lots of reflections.
Using Bluetooth would also be possible in urban areas as well. E.g. you can often pick up Bluetooth from devices such as Smart TVs and home stereo systems, which gives you very good location accuracy because of the low range of Bluetooth. (I read that Google was investigating this, I don't know if they actually do it. In my building, this would give enough accuracy to pinpoint the floor and the corner of the building.)
This means that Google has very accurate position and signal strength information for pretty much every WiFi access point in the entire world, and the same for mobile towers.
Now, with Power Save Mode, this process is simply reversed. Your phone uploads all WiFi and mobile base stations with their IDs and signal strengths, and instead of using the positions of multiple phones to fix the location of a base station, Google now uses the positions of multiple base stations to fix the location of your phone.
An alternate possibility would be to try and find a phone that has seen the same set of stations with the same signal strengths before, and had GPS turned on, so we know what its location was, and we can guess that your location must be close.
So, in short, Google relies on a database of mobile and WiFi base stations. Data from phones that have Power Save turned OFF is used to determine the locations of those stations from the locations of the phones, which then allows Google to determine the location of phones with Power Save turned OFF from the locations of those stations.