What does 'zero-mean random noise with standard deviation equal to 1' mean? Can anyone tell me what the meaning is of the phrase: "zero-mean random noise with standard deviation equal to 1"?  Also, I want to know why not except zero-mean random noise and standard deviation equal to 1. 
Why should I use zero mean and std 1?
An example of the context is from the following paper:
II. OBSERVATION MODEL
We consider an observation model of the form
z (x) = y (x) + σ (y (x)) ξ (x), x ∈ X, (1)
where X is the set of the sensorís active pixel positions,
z is the actual raw-data output, y is the ideal output, ξ is
zero-mean random noise with standard deviation equal to 1,
and σ is a function y, modulating the standard-deviation of
the overall noise component. The function σ (y) is called
standard-deviation function or standard-deviation curve. The
function σ2 (y) is called variance function. Since E {ξ (x)} =
0 we have E {z (x)} = y (x) and std {z (x)} = σ (E {z (x)}).
There are no additional restrictions on the distribution of ξ (x),
and different points may have different distributions.
 A: Zero mean so that the noise does not present a net disturbance to the system.  There's as much positive noise as negative, so they cancel out in the long run.  If the mean were not zero, then the noise would appear as an additional dynamic.  For example, if the quantity were a force with some random jitter to it, then if the jitter did not have zero mean, the noise would appear as an additional net force on average.
Standard deviation 1 means that the variable has been scaled for convenience.  Going back to the force example, one would typically find that the std of the force is some value in Newtons.  .01 N,  1 N,  1,000,000 N, whatever, depending on the problem.  It is sometimes valuable to rescale the random force by dividing by the standard deviation.  This has the effect of making the force dimensionless:  Newtons divided by Newtons.  It also allows for the calculation to be used for forces at any scale.  The solution becomes more easily generalized to other situations.  It also creates a notion of "characteristic force".  The force is measured with respect to the value of the characteristic force of the system.
There are other ways to define characteristic values, and thus other ways to remove dimensions from the equation.  Evidently in the case you cite, the author has decided that the standard deviation of the noise is convenient for his purposes.
