what is a Gaussian signal?
The stochastic description of signals is realized by random processes. The book you cite actually speaks of a Gaussian random process. By definition, every random variable drawn from that process has a Gaussian probabilty density function. Mathematically speaking: let $\mathbf X(n)$ be the random process representing the signal, then for every $n_1$ the random variable
$$
X=\mathbf X(n_1)
$$
is Gaussian distributed. This in turn means, that $X$ has the probability density function
$$
p_\mathrm X (x) = \frac{1}{\sqrt{2\pi\sigma^2}}\mathrm e^{-\frac{(x-\mu)^2}{2\sigma^2}},
$$
where $\mu$ and $\sigma$ are the mean and standard deviation of $X$, respectively.