A moment is … a measure of … the shape? of a function?
Populations have moments, Samples have moments, and these moments relate to each other.
$K$th population moment = $\mu _ k$ = $E(X^k)$
$K$th sample moment = $m _ k$ = $\frac 1 n \sum (x_i^k)$
$\mu _ 1$ = $E(X^1)$ = Population Mean
$m_1$ = $\frac 1 n \sum (x_i)$ = $\bar x$ = Sample Mean
Estimate $\theta _ 1 , \theta _ 2 , … \theta _ k$
Solve the System of Equations $\mu _ k = m _ k$
Finding the estimator for one parameter is easy. Finding two is harder, as it becomes a system of equations.
See the exponential example.