The Action head offers the fastest flash duration of the three flash heads. At full power on an ELB 400, these heads offers a t0.5 flash duration of 1/2800th second. That fast flash duration can stop motion quite effectively when shooting at the standard flash sync of 1/200th second.
If you are shooting in low light and want to drag the shutter, i.e. use a slow shutter speed like 1/15th second, but also want to stop the motion of a moving subject, then the Action flash head is the one you want. Keep in mind that this head is not recommended for use with Hi-Sync
Below, you can see an example of this type of image, where the shutter speed was set to 1/20th second and the aperture was set to f/5.6. The fast flash duration froze the mountain biker at the top of his jump. But, as you can see, there is some ambient light bleeding through as well - this is the motion blur of the subject represented by the dark shading in front of him.
The subject is sharp, stopped by the fast flash duration, but the subject's shadow was tracked by the longer 1/20th second shutter speed. When shooting this type of image the motion blur is always going to be there no matter how fast your flash duration is. Whether or not the motion blur is in front or behind the subject is a matter of how the flash was synced, either using front curtain sync (standard sync) or rear curtain sync (a.k.a. 2nd Curtain Sync for Canon shooters).
Note that if you used a flash head with a slow flash duration, like the Pro head, which has a flash duration of 1/1200th second at full power, then the cyclist would not be sharp because the flash duration was not fast enough to stop his motion.
Another situation where the Action head shines is when shooting with medium-format cameras, which can sync with flash at up to 1/1.600th second with no games. For this to work well, a fast flash duration is required. In fact, a flash duration that is shorter than the shutter speed being used is required. So this means that you need a flash duration faster than 1/1600th sec., and this is where the Action head comes in handy.
When shooting with a Hasselblad H5D, which can sync up to 1/800th second, the Action head is very useful.