It is similar to a Wizard's staff, except it's like a Blackberry to the staff's 3GHz laptop. The wand allows a witch to perform some powerful magic on the spot, if they know how to use it. Its main power involves turning things into other things- for instance, Lily Weatherwax uses hers to turn two snakes into human women, and Magrat uses hers to make a lot of pumpkins.
Desiderata Hollow, a good Witch and Fairy-Godmother, possessed a magic wand. Upon her death in Witches Abroad, both Granny Weatherwax and Nanny Ogg came to her cottage to try and find it, but in fact she had sent it to Magrat Garlick, with a note that she needed to go to Genua and stop a servant girl from marrying a prince. Magrat first attempts to use the wand in a collapsed Dwarf mine by wishing for something to happen. She is able to turn rocks that were covering a valuable vein of gold-bearing quartz into pumpkins. Future attempts prove that the only thing she can do with the wand is turn other things into pumpkins.
She also used it as a blunt object against the two snakes in human form (the ones created by Lily). The blow turned them back into snakes... just in time to meet a small furry animal in the corner of a room that happened to be a mongoose.
Lily Weatherwax, as the bad Fairy-Godmother, also possessed a magic wand, but was far more skilled with its use. She used it to undo a number of changes made by Magrat that were intended to stop Ella from going to the Ball, as well as to make the two aforesaid snakes into humans.
After the Happy Ending, Granny Weatherwax asks for the wand, and promptly uses it to create flowers. She tells Magrat that the key isn't simply to wish for things to happen, but rather to work out how to make them happen.