Signal generation: random noise
The phrase "zero mean" is primarily a phrase from the mathematical field of statistics.  For us, a "zero mean" sequence means a sequence of numbers whose mathematical average is zero.

By the way, MATLAB's randn(1,N) command does not generate exactly a zero mean sequence. It generates an N-length sequence of random numbers that fluctuate randomly above and below an amplitude of zero, but the sequence's mean is not guaranteed to be zero.  The larger is N the closer the average (mean) of randn(1,N) will be to zero.  Try these: 

mean(randn(1,5))  and  mean(randn(1,500))

I have no idea what "the amplitude interval (0,0 1,0)" means.