This is a general question. I would like a better conceptual understanding of what a moment is, it's meaning, and it's applications (not just in probability).
I already looked at Wikipedia, but I still didn't understand it. Could someone explain it in simpler terms?
In some generality, given a measure $\mu$ on $\mathbb R^n$, point $a \in \mathbb R^n$, and multi-index $\alpha$, the corresponding moment of $\mu$ is
$$\int (x - a)^\alpha \; d\mu(x) $$