The insect wars were a period of history in which humanity came close to being wiped out by Insect Civilisation, a race of vacuum capable, resilient and cunning creatures. It is unknown who began the war or why, though evidence suggests that they may simply have an innate hatred for other races, requiring them to either destroy, or subjugate other species by their very nature.
Little is revealed of the exact events of the war, except that the Brunnen-G fought against, and ultimately defeated the insect race. It is unclear exactly how they achieved this given how powerful the insects appear to be when considering the abilities of the Giga Shadow, however while the crew of the Lexx try to decide how to fight Mantrid in Lexx 2.20 "End of the Universe", Kai comments that the insects were methodical, and therefore predictable. It is therefore likely that the insects may have been ambushed in a Brunnen-G assault.
In Lexx 1.1 "I Worship His Shadow", the Divine Predecessors and the Time Prophet describe a prophecy that foretells the final outcome of the insect war, including that the Insect Civilisation and the Divine Order would ultimately be destroyed in the hands of the Brunnen-G.