Difference between low signal and no signal for a SR latch?
When an input has designation 0, this means "low signal" correct? 


Uh, usually.  Sometimes people will work with "negative true" or "active low" logic, which doesn't change the parts, it only changes the meaning of the voltages.


  Is this completely different than "no signal"? 


Yes and no.  When you're talking boolean logic there's only two possible states.  When you're talking electronics, the "gates" act like high-gain amplifiers.


  Doesn't a logic gate need some kind of signal in both input wires in order to produce an output signal?


Uh -- beep, does not compute.  See above.  There's always a "signal".


  If so I don't understand how an SR latch can ever product any kind of output. Even if we sent signal in through S and R at the exact same time, neither one can produce an output until the other input receives a signal, but they both rely on each other for this.


Look at the logic elements as if they're circuit elements.  When you turn on the power, the latch is in some unknown state, or it may even be in a real live indeterminate state, with both outputs stuck in between low and high.  Now think of those two NOR gates as amplifiers with negative gains of amplitude more than one.  If one of those outputs is just a bit above center, it'll cause the other output to drive down, which will drive the one output even higher, and the latch will quickly settle into one state or another.

(A similar thing happens if you tie the S and R inputs together and toggle them simultaneously -- with both inputs high, the outputs are held low, but it's like balancing a penny on a needlepoint.  As soon as the inputs go low the outputs will fight briefly, then the latch will go to one state or another).


  At the same time it can't be "no signal" either because this would imply the NOR gates could send a signal even when no power is being sent through.


There is no question mark here, but I think you're unclear on the concept of power vs. the concept of signal.  In the real world, the gates would be powered; in the theoretical world, the gates just magically act the way they do, without requiring power.


  Where is my understanding wrong?


I'm not sure.  But I hope that I've clarified things.