This is a simple one-transistor voltage regulator.
The incoming supply will have .6V subtracted from it.
The green led starts lighting when the load gets 3V or so.
The red led comes on when the incoming supply is great enough to send current through the led and zener diode.
the green led will stay lit if the voltage stays above 3 to 3.5 volts and switches red if the voltage drops below 3 or 3.5 volts (haven't decided on a ceiling or floor voltage).
There are simple circuits where a single transistor can alternate between 2 led's based on the supply voltage.
However given your low operating voltage, the red led will just about start to illuminate at 3V.
Furthermore notice there are green led's which need a higher voltage (over 3V) to illuminate them, as compared to red led's (1.7V). If you have such a green led, you may as well hook it up to the supply separately from the red led.
Each should have a safety resistor inline, between 330 and 470 ohms, depending on maximum expected voltage.