What are you really measuring as a battery discharges?

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Think for example a phone or any devices that shows the amount of battery power is left. It shows it as a graphic where you can deem whether it's full, 3/4 full, 1/2 full, 1/4 etc... or shows the actual percentage. What is that measure really showing you? Voltage? Amp hours left (which is the capacity I think)? And, how is it calculated?
 
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As a battery discharges the voltage drops under load. This is mostly due to internal resistance increase.
http://www.mpoweruk.com/soc.htm discusses it. It's possible to monitor this externally.

But. most LI-ion batteries have an internal monitoring circuit that reports charge and discharge data back to the operating system. This is best because the data is so battery dependent.