What are Autoregressive Coefficients? Can anyone explain what are Autoregressive Coefficients? What is their meaning that is.

Consider a method:

public double[] calculateARCoefficients(double[] inputseries, int order)

When this method is called on 256 values, lets say these values represent some kind of signal, I will get an array of n numbers, where n=order. What do these numbers represent?

I mean for example variance tells me how spread out the values of the signal are. The higher variance value is, the more spread out values are. The smaller variance is, the more unified signal is.

Are you able to say, in a similar fashion to above paragraph about variance, what value of AR coefficients says about the signal?
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.