It's a bit tricky. Here's the basics:
The McAuliffe Ambush was *essentially* the start of the Terran-Kilrathi war. Confed declared war on the Kilrathi on 2634.186 -- with the intention of fighting a 'limited war' to teach certain Kilrathi groups a lesson following violent pre-war piracy. The war was limited to actions in only the Facin Sector, and there were no major engagements. Confed lacked serious data on the empire, but considered them "a third rate power", and believed that the Emperor and company weren't involved in the war.
On 2634.235, Confederation Day, the Kilrathi struck Confed's largest outer base -- the docked Third Fleet at Alexandria Station and the military base on Johnson's Island, on McAuliffe. No one expected the attack, and the devestation was horrific -- 70 warships were lost, Confed's most powerful starbase destroyed, and the Kilrathi were landing marines.
Confed learned of the attack just before this, but a serious of accidents kept the orders to keep the base alert from arriving in time. Admiral Banbridge had wisely ordered a task force group to McAuliffe immediately -- Rear Admiral Dayan's TCS Ark Royal and escorts. But the translated information on the attack had been wrong -- it reported only a fraction of the number of enemy forces.
Admiral Dayan's group succesfully extracted the TCS Concordia, the surviving Confed carrier, and several battleships and smaller craft from McAuliffe. The decision was made for Ark Royal and Concordia to launch a strike against the Kilrathi invasion forces -- in hopes of crippling the enemy landing craft and forcing a Kilrathi withdrawl. The small Confed force didn't stand a chance against the Kilrathi -- they took heavy losses... but they took out the enemy marines during their attack. The Kilrathi were forced to withdrawl, ruining their plans to launch a massive offensive and take the Confederation immediately. Confed's losses were horrific -- they're most impressive fleet gone, well over 100 other systems taken by the Kilrathi... but the enemy spearhead was broken. The two sides settled in for a long war.
A war that would again involve McAuliffe.
On 2639.033 Kilrathi forces invaded Enyo and McAuliffe, holding human colonists hostage on the two worlds using orbital gunships. Confed replied with a brilliant tactical maneuver. They first sent a force of Raptors to the systems, carrying extra space mines. The Raptors do not threaten the Kilrathi -- they deploy their mines at the system jump point while the Kilrathi waste time and lose organization hunting them down. At an exactly timed moment, the mines explode -- and a Confederation fleet jumps in. The fleet immediately engages the gunships, saving the colonists. The two fleets engage in a traditional fleet action, and both take similar, heavy losses. The Kilrathi, however, retreat again...
In 2654 the Kilrathi attempted to raise a fleet in Vega to attack the Confederation colonies -- their objective: taking the Terran Knowledge Bank at McAuliffe's research installation. The TCS Tiger's Claw engaged enemy raiders at Enyo, and then moved to McAuliffe -- where they were unable to save the colony. Kilrathi forces finally took McAuliffe, and the Confederatino withdrew. The Kilrathi's days in Vega were, of course, numbered... but for a time, McAuliffe had fallen.