I was reading this answer that is talking about properties of $AA^T$.
If you center columns (variables) of $\bf A$, then $\bf A'A$ is the scatter (or co-scatter, if to be rigorous) matrix and $\mathbf {A'A}/(n-1)$ is the covariance matrix. Pairwise formula of covariance is $\frac{\sum c_xc_y}{n-1}$ with $c_x$ and $c_y$ denoting centerted columns.
The answer didn't provide any definition of centering here. I have some guesses that it means to subtract the mean of each column from itself, but because I'm not a mathematician I'm afraid that my guess is wrong. So I'm here to make sure the correct definition.