What features give reason for such a wide range of prices for digital multi-meters?
What features give reason for such a wide range of prices for digital
  multi-meters?


THE most important feature is stability aka the voltage reference internal to the device. A lot of really good multimeters use the LTZ1000. Here's a picture: -



Notice how the device is mounted on spindly bits of PCB legs to avoid stress on the die causing random ppm shifts in the output voltage. If you read up on it you'll also find that it has a resistive heat generator and temperature sensor internally so it can be oven controlled.

The LTZ1000 boasts temperature drifts of 0.05 ppm per degree centrigrade. The best "off-the-shelf" device I've found is a maxim device at 2ppm/degC or the LTC6655 also at 2 ppm/degC. Long term stability is also top of the list when it comes the the voltage reference.

Next is very tight precision low drift resistors in fact matched resistor pairs like you can get from Vishay and Linear technology. These are not cheap and turn a run-of-the-mill meter into something like a decent fluke or HP meter.

Forget features - they are ten a penny in comparison.