For anyone who may not know, this is how a laser works...
The above link gives you the basics for lasers. It explains excitation at the atomic level. In addition, it explains the specifics of laser light. Also, the link gives a common example of a laser with its main parts.
Pulse lasers include everything in a normal continuous wave laser only with a little something extra. Pulses can be achieved by two main methods: Q-switching and Mode Locking.
Q-switching is used to gain pulses, but not the shortest pulses. The above link goes into detail about q-switching. It expresses active and passive q-switching along with application.
Mode locking is a different method used to pulse lasers and the shortest pulses can be gained using this method. The above link breaks down mode locking including how it works and the difference between active and passive mode locking.
There are many uses for pulse lasers.
This video shows a practical application of a pulse laser by the NAVY. They use it as a directed energy weapon system. Specifically, it is utilized to combat drones and other unmanned aircraft/weapons.
Another application of a pulse laser is as a "toy." While no high power laser is a toy, this particular laser has no use other than it's pretty cool. This is a homemade pulse laser gun. it fires a short infrared pulse that is powerful enough to melt plastic.