Correlation Performed by Convolution
What that statement is saying that 

a. Correlation is performed the same way as one would perform convolution (you must implicitly know that one of the sequences is conjugated and time reversed to express a correlation as a convolution, as it was not stated there),

and

b. Mathematically the convolution is performed using this relationship

$$x[n]*h[n] = \mathscr{F}^{-1}\left\{\mathscr{F}\left\{x[n]\right\}\cdot\mathscr{F}\left\{h[n]\right\}\right\}$$

Where $*$ denotes convolution, $\mathscr{F}\left\{f[n]\right\}$ denotes the Discrete Fourier Transform of $f[n]$, and $\mathscr{F}^{-1}\left\{F[k]\right\}$ denotes the Inverse Discrete Fourier Transform of $F[k]$.

Note that these operations with Discrete Fourier Transforms actually yield the "circular" convolution of $x[n]$ and $h[n]$, which is equal to the linear convolution of $x[n]$ and $h[n]$ only under a certain condition: there must be enough zero padding to avoid aliasing.