The UR20s also, by the way, have only 32 ohm impedance, which is important when you want to run headphones from equipment with weedy headphone outputs. The crummy headphone sockets in most home and portable stereo gear can't deliver a whole lot of power (by headphone standards - most headphones need a fraction of one per cent of the power of a loudspeaker), and often have serious voltage and current limits, too.
A strong headphone amp, such as you'll get in some quality hi-fi gear, and in pretty much any dedicated headphone amplifier, can drive all but the very strangest headphones as loud as anyone needs. If you've got headphones with very high impedance, though, you'll need a lot more output voltage to drive them to reasonable volume. More than a few high-end headphones have 600 ohm impedance, for instance; most headphone sockets can't get much volume out of those at all.
Voltage equals current times resistance (impedance is the more complex AC incarnation of resistance, but the simple DC version will do for now, and reduce the number of readers' heads that go round and round), and power equals voltage times current. So to drive a 32 ohm headphone transducer to, say, five milliwatts (mW; 0.005 watts), you need 0.4 volts. That'll result in 12.5 milliamps (mA; 0.0125 amps) of current flowing (as long, once again, as you ignore the Nasty Math that's involved in real world multi-frequency AC power calculations, and also as long as you remember your algebra. Otherwise, the numbers may turn out quite differently).
Step up to 600 ohms, and now five milliwatts requires 1.73 volts, with less than three milliamps of current flowing.
If the 600 ohm headphones are much more efficient than the 32 ohm ones (efficiency is the amount of noise you get per milliwatt; the UR20s are rated at a better-than-OK 97dB from one milliwatt input) then you'll be able to play 'em pretty loud even if your headphone output only goes up to 1.5 volts, but if the efficiency figures are much the same (as they often are, these days) then the 32 ohm 'phones will play considerably louder from a voltage-restricted headphone output.
12.5 milliamps isn't a great deal to ask for from practically any headphone socket, but more than 1.5 volts may well be; small battery powered devices, in particular, commonly don't go that high, at least not without nasty distortion. For them, low impedance headphones are definitely the way to go, particularly if you're buying at the bargain end of the market and so even a cheap add-on headphone amplifier is totally not an option.
