Dragonrend is a Shout devised by early Nord Tongues to help battle dragons like Alduin. The Shout was designed to force mortality upon dragons. In practically use, it shackles dragons to land temporarily, leaving them open to more opportunities to being attacked by those more bound to the land.
As the Shout was specifically created to leverage a concept that dragons cannot possibility comprehend, dragons themselves cannot learn it for their own use. It was in effect created to be a weapon to be used against dragons when they threatened Skyrim in the distant past.
 In Game Use
All three words of Dragonrend are learned at once by the Dragonborn during the quest Alduin's Bane, when s/he must use the Elder Scroll at the Time Wound near the peak of the Throat of the World to witness the moment Alduin was first banished from Nirn by the early Nord Tongues Gormlaith Golden-Hilt, Hakon One-Eye and Felldir the Old.
While Dragonrend does not deal any damage to dragons themselves, any dragon hit by the Shout will be land for a short period of time. It is a very useful and powerful tool in the Dragonborn's arsenal, even if s/he is skilled at attacking airborne dragons by means of magic or archery.
It is important to note that while the dragon is unable to move during the period it is bound to the ground, it is still more than capable of retaliating against attackers; as always, beware of those nasty bite attacks!