Thevenin Resistance?
The Thevenin resistance is the amount by which something's voltage will change if the current changes by a certain amount, and he is assuming that the voltage drop across the LED will be 2.0 volts whether one puts one microamp or one mega-amp through it.  If the voltage across the LED doesn't change at all with respect to current, then the effective resistance is zero.

In practice, the voltage drop on real LEDs isn't constant.  A somewhat more realistic LED model might drop 1.8 volts plus 0.02 volts/milliamp (so at 10mA it would drop 2.0 volts, at 20mA it would drop 2.2 volts, etc.)  If one side of an LED is connected to a fixed voltage source, the other side would have a Thevenin resistance of 20 ohms (20 volts/amp).  Note that with any sort of real LED, the Thevenin resistance will change with current.  If it were fixed, an LED whose behavior was as described above (assuming infinite precision on the above numbers) would drop 1.80000000002 volts with one picoamp flowing through it, and would drop precisely 20,001.8 volts with one mega-amp flowing through it.  In practice an LED with only a picoamp flowing through it would drop almost no voltage, and an LED with a mega-amp flowing through it would have an essentially unmeasurable voltage drop (since it would be an unenclosed cloud of plasma).