What does $μ_{22}$ stand for in the formula for the variance of a covariance estimate?
I gather that $μ_{11}$ is the covariance of variables X and Y, $μ_{20}$ is the variance of X, and $μ_{02}$ is the variance of Y, but what is $μ_{22}$?
The formula can be found here: https://stats.stackexchange.com/a/48393/20385
On the assumption you seek interpretation rather than the formula for central mixed moments (since that's already available at the linked question), one way to look at $\mu_{22}$ is that it is the covariance of the squares of the centered variables plus the product of their variances. i.e.
$E[(X-\mu_X)^2(Y-\mu_Y)^2]=\text{Cov}[(X-\mu_X)^2,(Y-\mu_Y)^2]\,+\, \text{Var}(X)\,\text{Var}(Y)$
Further, note that when it is standardized by dividing by the product of the variances (in similar fashion to turning a covariance into a correlation, $\frac{E[(X-\mu_X)^2(Y-\mu_Y)^2]}{\sigma_X^2\sigma_Y^2}$ is one of the three measures referred to as co-kurtosis (specifically $K(X,X,Y,Y)$).
See here: https://en.wikipedia.org/wiki/Cokurtosis#Definition
As we move up to the higher moments (and this is essentially a bivariate moment of fourth order), direct interpretation of unstandardized moments becomes more difficult in a similar way to trying to interpret the 4th central moment directly (rather than standardizing to the kurtosis) becomes difficult.
(Indeed, even interpreting kurtosis is difficult - most interpretations of kurtosis given in textbooks are incorrect or misleading.)
Let $(X,Y)$ have joint bivariate pdf $f(x,y)$. Then $\mu _{r,s}$ typically denotes the product central moment:
$$\mu _{r,s}=E\left[(X-E[X])^r (Y-E[Y])^s\right]$$
