What is Covariance matrix, sample covariance matrix?

The covariance matrix of a random vector $r \in \R^N$ is $\Sigma = \E[(r - \mu)(r - \mu)^\top]$. From $T$ observations $r_1, \dots, r_T$ with sample mean $\bar r$, the sample covariance matrix is $S = \frac1T\sum_t(r_t - \bar r)(r_t - \bar r)^\top$ (or with divisor $T - 1$).