The Wizard's Wand is a device created by Cisco Ramon to combat Mark Mardon, nicknamed "Weather Wizard". It's designed to suck up excess electrons in the atmosphere, preventing any form of weather from occurring, in order to combat Mark's atmokinesis. However, it has also been shown that Mardon can use the wand offensively as a means to channel his powers more precisely.
In order to easily fight the Weather Wizard, Cisco Ramon created the Wand. It was given to the Central City Police Department to place in the middle of the building if Mark came near. However, he shockingly appeared following its installation, catching them off guard. They were unable to use it and Captain Singh was paralyzed, before The Flash sped in and used it to prevent the weather inside, making Mark flee. Then Barry restarted the timeline and captured Mark right away, so the device was never created.
When Mark returns and breaks both James Jesse and Leonard Snart out of prison, a new model of the Wizard's Wand was created by Cisco Ramon and Jay Garrick out of Barry's knowledge of the altered timeline in which Mardon created a tsunami to devastate Central City. After Cisco, Jay and Harrison Wells managed to send all of the bombs The Trickster gave kids while posing as Santa Claus into the breach, Barry shocked Mardon with the wand and defeated him. 
Cisco later used the wand to generate a bolt of lightning to help recreate the conditions under which Barry became the Flash to restore Barry's powers after they were stolen by Zoom.
In a confrontation with Weather Witch, Barry used the Wizard's Wand as a means to absorb the lightning cyclone the former had created with her staff. When he'd absorbed the electricity she'd generated around her with her staff, she tried firing another bolt of lightning from the staff directly at him, but he countered it by throwing a lightning bolt of his own at her, and subsequently took her into custody.
Behind the scenes
- In DC Comics, Weather Wand was used by Mark Mardon as a weapon to control the weather in the vicinity as opposed to stop him from using is powers. In the comics, the wand was created by Clyde Mardon.