Does the remaining miles (kilometers) display represent the distance left before the vehicle will literally run out of gas, or is it the range before the "reserve" fuel - typically 1.5-2 gallons - starts?

 

The calculation is pretty "soft", not very precise and in my experience quite pessimistic in that it
displays considerably fewer miles than could theoretically be driven. Remember that most car
companies pay for Roadside Assistance for some period and they don't want you stranded any
more than you do!
Look up the nominal fuel tank capacity of your car and the next time you hit the Low Fuel Warning
subtract the next fill up quantity. That will be your reserve. With the Chevrolets I used to sell and
drive you could "weave" back and forth and the gas gauge would fluctuate if you had enough
fuel to slosh around and not move when you were seriously low. The gauges are now much
better damped and do not tend to vary as before.

 

From the time your range zeros out, you have roughly 2 gallons of fuel left in the tank. I've done 40 miles after that happened.

 

I have the 300h, with a 14.8 gallon tank... I ran it down to a range of 25 miles left, and put just under 12 gallons in the tank, implying there were ~2.8 gallons left... .8 to get me those 25 miles, plus a 2 gallon reserve. Makes sense! Until I filled up that is. I filled up, and it then stated I had a range of 510 miles... 510/14.8 = 34.4 miles per gallon, which is about EXACTLY what my trip computer says I average (as a former Prius owner)... so when the tank is full, it considers those 2 gallons in reserve, but when the tank is near empty, it does not? Seems strange ...