The order of rotational symmetry of a square is $4$.

Rotational symmetry describes the number of times a shape appears unchanged during a complete $360$-degree rotation. For a square, this means that when it is rotated around its center, it looks identical at four distinct positions. These positions correspond to angles of $0$ degrees, $90$ degrees, $180$ degrees, and $270$ degrees. Each of these rotations results in the square assuming a configuration that is indistinguishable from its original orientation.

To illustrate this concept, imagine placing a square on a piece of paper and marking one of its corners. When you rotate the square by $90$ degrees, the marked corner moves to the location of the next corner, yet the overall shape of the square remains unchanged. Continuing this rotation to $180$ degrees, then $270$ degrees, and finally returning to $360$ degrees (which brings it back to its starting position) demonstrates that the square retains its appearance at each of these angles.

This characteristic grants the square an order of rotational symmetry equal to $4$. Understanding rotational symmetry is essential in geometry, as it reveals the intrinsic symmetrical properties of shapes, which can be crucial in various applications ranging from design to solving mathematical problems. Thus, whenever you encounter a square, remember that it can be rotated four times within a full circle and still maintain its identical appearance!