Studying for the PSTAR I see that a flashing green signal while in the circuit means "return for landing" but this is not actually defined anywhere. What does that mean?
NORDO = "is an aircraft flying without a radio"
... because they could not communicate with you, but they wanted you to not land on this pass (interval a mess, crossing traffic, winds maybe wrong, a dozen other things that might crop up) it was more or less "the runway will be ready for you if you take another lap in the pattern." This also gives them a bit of time to get all of the other aircraft in the pattern out of the way of the aircraft in distress. (And the steady green ought to confirm that on the next pass, if all things go well).
Tower operators would rather get that aircraft who can't talk to them onto the ground. What they want to avoid in this case (again, this is what I was taught by a salty old Navy controller when I was in flight school) is that they wanted to avoid the aircraft attempting to land being "spooked" by a red light and thinking they can't land at this field. And then waving off and flying off in search of another field while still NORDO.
The green light is the 'friendly' light between choices of red and green. Put in the chief's colloquial jargon: "Flashing green lets the pilot know "the runway will be there for you when you come back for your next approach."
The teaching that I got may no longer be current, but the lights shown to a NORDO airborne aircraft still mean the same thing as they did when I was taught.
Steady Green: cleared to land
Flashing Green: return to land (to be followed at the proper time by steady green)
My understanding of light gun signals was taught to me a little differently. For simplicity, I will concentrate on light gun signals for airborne aircraft only.
So to put it into a nutshell that may be easier to remember:
The answers above are pretty much correct, but it is nice to cite sources.
Since the question is relating to studying for a PSTAR and is tagged Canada, first the Canadian sources:
Canada
Aeronautical Information Manual (Canada)
Section 4.2.11 Visual Signals - Aircraft on Ground
4.4.7 Visual Signals - Aircraft in Flight
United States
The Canadian signals are similar, but not exactly the same, as US FAA ATC signals, so adding these for US pilots who find this question
In the Airman's Information Manual (US FAA), the signals are described in Section 4-3-13
Differences
Logically it would seem to mean to fly a circuit around the traffic pattern and watch for a steady green light on the next final approach.