If the robot's orientation is fixed, then determining its linear displacement is sufficient to determine its location in the world. This is because one unit of "forward" on the robot is equivalent to one unit of "forward" in the world.
However, when the robot is allowed to rotate, one unit of "forward" for the robot now corresponds to a partial unit "forward" and a partial unit "sideways".
The clearest way to imagine this is to imagine that the robot has rotated 180 degrees, such that it is looking in the direction opposite to that which it had when it started. Now one unit of "forward" for the robot actually translate to one unit of "backward" in the world. Similarly, one unit of "left" now corresponds to one unit of "right" and vice-versa.
In this manner, local coordinates, as established relative to the robot, are only useful when the orientation of the robot is known relative to the world. If you don't know which way you're pointed, you can't know which way you're moving.