What is product σ-algebra?

For measurable spaces $(X, \mathcal A)$, $(Y, \mathcal B)$, the product $\sigma$-algebra $\mathcal A \otimes \mathcal B$ on $X \times Y$ is generated by the rectangles $A \times B$ ($A \in \mathcal A$, $B \in \mathcal B$) — a $\pi$-system. For $E \subseteq X\times Y$ and $x \in X$, the section is $E_x = \{y : (x,y) \in E\}$; for a function $f$ on the product, $f_x = f(x, \cdot)$.