What does standard deviation of noise 1 mean?
Your question is too basic, and it gives the impression that you haven't done enough study of the subject on your own. I'll provide a few hints:


To understand noise, you first need to specify its probability distribution. I assume you're refering to Gaussian noise in your question, but not all noise is Gaussian. In particular, in digital capture of an image, there are several kinds of noise present.
Gaussian noise is specified by its mean and its variance ($\sigma_n^2$) or its standard deviation ($\sigma_n$). The physical interpretation of the variance is that it is related to the noise power. There is nothing special about $\sigma_n=1$.
Most computer random generators (for instance, Matlab's randn) generate samples of a Gaussian random variable with zero mean and variance 1. It is easy to convert this random variable to another Gaussian random variable with any specified mean and variance.
You need to understand the effects of clipping Gaussian noise. Think about a sensor photosite being pulled or pushed beyond its dynamic range by the noise. However, as I said in another answer, the resulting noise is no longer Gaussian.