What are Autoregressive Coefficients?
The coefficients $a_i$ of an autoregressive (AR) model of a signal $x(n)$ enter the model definition in the following way:

$$x(n)=\sum_{i=1}^Na_ix(n-i)+e(n)$$

where $e(n)$ is zero-mean white noise and $N$ is the model order. I.e. the signal is modeled as the output of a linear time-invariant filter with transfer function

$$H(z)=\frac{1}{1-\sum_{i=1}^Na_iz^{-1}}$$

and with input signal $e(n)$. There is no simple interpretation of specific values of the coefficients $a_i$. You have to look at the whole polynomial $1-\sum_{i=1}^Na_iz^{-1}$, e.g. by computing the power spectrum of the AR model of $x(n)$:

$$S_x(z)=\sigma_e^2\left|\frac{1}{1-\sum_{i=1}^Na_iz^{-1}}\right|^2,\quad z=e^{j\theta}$$

where $\sigma_e^2$ is the variance of $e(n)$. So the AR coefficients are the parameters of a specific signal model, and they do not have a simple interpretation comparable to mean or variance of a random process. However, in general they represent a much more detailed description of the signal than mean and variance alone.