The units themselves aren't terribly complex. The valves use the pressure of the water to open and shut. There is a small solenoid with a mechanism similar to a retractable ball point pen. One surge of power, clicks open, second surge, clicks shut. The rest is a simple motion detector. For a sink this is just a photocell that measures the light reflected off the sink bowl. When the light drops the circuit runs the solenoid.
There are variations in design. May run for X seconds. May run for Y seconds after the light returns to normal. May have a max of Z seconds.
Anyway: Simple design + large quantities + low cost = low resource usage (first approximation)
So the next question: Do they save water? A faucet with an aerator screen (makes the volume seem greater) runs about 2 liters a minute -- a cup every 5-8 seconds. Most bathroom hand washers are really hand rinsers, and only run the tap for a few seconds. Probably a large fraction use under 1/2 cup about 1/8 of a liter.
Payback: Another post mentions buying used ones for 60 bucks. Used plumbing at our local habitat for humanity Re-store tends to run 1/3 to 1/2 of new costs. Suppose a new one was $300. If water is scarce you may be paying as much as $5/cubic meter, or .5 c/liter (For comparison, my cost is about 10 c/cubic meter) Suppose that motion activated cuts water usage in half, to 1/16 of a liter. 32 handwashes per liter saved. 32,000 hand washes per cubic meter, 192,000 hand washes to pay for the faucet. If they have a 5 year life span, that's under 40,000 per year, about 5 per hour in a 24 hour facility, like an airport.
If water is cheaper (likely) the payoff is longer.
Compare this to the 1 gallon (4 liters) used to flush a toilet, or the 1 liter to flush a urinal, this is small usage. Add to that some large fraction of people don't wash their hands.
From a sustainability standpoint this is NOT low hanging fruit. Automated urinals that were smart enough to flush only every 3-4th usage if urine was close to clear would save more water. Or a system that used a mist to rinse down the sides of the urinal. Or a downdraft air current that whisked away the stink using no water.
Motion activated faucets have other merits: Conventionally, people with soiled hands are turning the faucet on, washing their hands, then turning the faucet off, recontaminating their fingers. More significantly, they are doing so with not just their germs, but with strangers germs. It may actually be safer to NOT wash your hands -- you are likely used to your own germs, and contacting people with only one set instead of 50 sets may be safer for them too.