What is Doppler Spread
I had the same question, and by reading http://www.wirelesscommunication.nl/reference/chaptr03/fading/doppler.htm I think the following is the answer.

1) Imagine you transmit a short burst of a sine wave of a fixed frequency.

2) When there is no relative motion between the transmitter and the receiver, due to multipath the receiver can receive the same signal at different times, because a one copy took a short path and arrived quickly, another took a long path (header in a different dircection, bounced off a building, and reflected back toward the receiver).  This is multipath.

3) Now add relative motion to the scenario above. Because of the different incident angle, not only will the longer path signal arrive later, but it will have a arrive with a different incident angle, and therefore (due to the Doppler Effect) it will have a different frequency.  So the Doppler spread would be the difference of the two frequencies received (even though there is only a single fixed frequency being transmitted).