The Hadamard product refers to component-wise multiplication of the same dimension. The $\odot$ symbol is commonly used as the Hadamard product operator.

Here is an example for the Hadamard product for a pair of $3\times 3$ matrices.

$$\left[\begin{array}{ccc}a& b& c\\ d& e& f\\ g& h& i\end{array}\right]\odot \left[\begin{array}{ccc}j& k& l\\ m& n& o\\ p& q& r\end{array}\right]=\left[\begin{array}{ccc}aj& bk& cl\\ dm& ne& fo\\ gp& hq& ir\end{array}\right]$$