The wave speed is how fast the wave travels. For example, you look at a wave crest on a slinky, the speed at which it moves is simply the wave speed.
The period is the time taken for a particular point on the slinky to complete one cycle of movement. For example, if a point was initially a crest, the time taken for it to move down and then all the way back up again is the period of the wave.
Hope this helps!
(published on 04/06/11)