The Khalai Insurgents, led by Judicator Aldaris, was a protoss terrorist group formed to attempt to overthrow the Dark Templar tribes on Shakuras lead by Matriarch Raszagal, who they (correctly) believed to be corrupted by the Queen of Blades.
Since Sarah Kerrigan's arrival to Shakuras, Judicator Aldaris was feeling uncomfortable. After a short briefing, Kerrigan agreed to help Raszagal, Artanis and Zeratul to recover the lost Uraj and Khalis crystals. However, Aldaris suspected something. He saw the alliance between protoss and Kerrigan's zerg as a defilement of Aiur's memory. Finally, shortly before the return to Shakuras of the Executor's expeditionary fleet sent to recover the Khalis and the Uraj, he somehow discovered Kerrigan's manipulation of Raszagal.
Secretly aware of this, Aldaris took control of an entire legion of protoss refugees, including virtually all of the remaining Conclave's warriors, and led them in an attack against Raszagal. The Matriarch returned the favor, launching an attack against Aldaris himself and allowing the creation of the forbidden dark archons. After fighting hard against the Conclave's loyal warriors, the Executor managed to overthrow Aldaris' force.
With the battle lost for the Khalai warriors, Artanis and Zeratul confronted Aldaris, avoiding his escape. After a really short meeting, Kerrigan appeared surprisingly with a force of lurkers and killed Aldaris, ending with the rebellion once for all.