A product is an expression of the form $a_1\cdot a_2\cdot\ldots\cdot a_n$ for a finite number of elements. This can be also written more shortly using the $\prod$ symbol:
$$\prod_{i=1}^n a_i.$$
If there are infinitely many number of elements we want to multiply, we write more generally $$\prod_{i\in I} a_i,$$ where $I$ is an arbitrary index set.