THe resistor is making a feedback loop for Q1 so it is dropping the extra voltage across it the same way the LM is dropping extra voltage in order to produce a lower, regulated voltage. Q1 and R1 are like an amplifier that is in parallel with the LM to increase current output. A1 is using the LM's regulated voltage in own feedback loop to imitate and assist the LM in current output capability.
The transistor is turned off and the regulator regulates low load currents.
When the current in the load increases then it also increases in the regulator and when it causes 0.7V across the 3 ohms resistor (0.7V/3 ohms= 233mA) then the transistor turns on and passes any more current.
If the output is shorted then the current will be extremely high and the transistor will be destroyed. A second transistor can be added to limit the max current.
You are not using the LM78xx to it's full potential change the resistor to 0.75hm: to work it a little harder and take some of the stain off the transistor. Of course, if you're using this for a high input-output voltage differential then stick with the 3hm: as the LM78xx limits the current to about 250mA at differentials over 15V.