First of all to answer a question you didn't ask, $\mu$ is the Greek equivalent of the latin $m$, which stands for mean.

Now for the question you did ask. If you have a random variable $X$, and let's assume $X$ is positive for simplicity, then you always have a mean $\mathbb EX$ (which could be infinite). The mean is computed mathematically, by integrating against the probability density function. Thus, both the variable $X$ and the mean $\mu=\mathbb EX$ are theoretical quantities. They describe the statitician's model of the quantity of interest.

On the other hand, the way experiments commonly work is that we collect a sequence of samples to try to nail down a more accurate model. Now the experiment as a whole can be thought of as a single random object, described mathematically by a probability distribution (or better yet, measure) on an infinite sequence space. The actual measurements taken can be written as an infinite sequence $(X_i)_{i\in\mathbb N}$. Now our model will usually posit that the measurements we take all have the same distribution ($X_i$ and $X_j$ have the same law, for all $i$ and $j$) and that the measurements are independent. In this case, the central limit theorem guarantees that if you compute the sample mean $$ \lim_{n\to\infty}\frac{X_1+\cdots+X_n}{n}, $$ this a priori random quantity will in fact converge (with probability $1$) to the theoretical mean $\mathbb EX_1$.

Thus, in the limit of a very large number of samples, there ceases to be a distinction between the theoretical mean of a single variable, and the sample mean of the whole population.