It means a rectangle. For instance if you call R^2 the x-y plane, then [0,1] X [0,1) would be the set of numbers where
[tex]0\leq x \leq 1[/tex]
and
[tex]0\leq y < 1[/tex]
Draw a square in R^{2} space with vertices at (0,0),(0,1),(1,0) and (1,1) and shade the box. The side edges and bottom edge are closed and the top edge is dotted. So any point on the top edge is not in the region [0,1] X [0,1).