When Abathur needed aid in controlling the chitha, a breed not connected to the zerg hive mind, he used Mukav to do this, giving her the rare ability among zerg to vocalize speech. It is not specified if Abathur created Mukav specifically for this task, or if she was a pre-existing queen that he modified to his purposes.
When Zagara asked Valerian Mengsk to come to Gystt, Abathur ensured Mukav was sent in Zagara's personal leviathan. Mukav relayed the request to Valerian and he accepted. For the duration of the events on Gystt, Mukav remained on the leviathan, commanding Abathur's forces including the chitha. When Abathur's deception was uncovered aboard the leviathan, Zagara confronted him while Mukav witnessed. The scene eventually turned violent and Mukav attacked the terrans accompanying Zagara. In the battle she was killed by Ulavu.
As a queen, Mukav could control lesser zerg breeds and communicate psionically. She possessed the ability of vocal speech, a rare trait among the zerg. It was for this ability that Abathur had her aid him, as the chitha, having no connection to the zerg hive mind, could not be controlled directly and needed vocal commands.
Mukav feigned simplicity upon relaying Zagara's message to Valerian, but was actually quite intelligent and independent. Despite this she was still a bit foolish, insisting on "translating" Zagara and Abathur's conversation to the terrans even though they informed her they could understand the two already; she expressed doubt that the terrans could grasp the "nuances" of what they were saying.