An Autarch is an Eldar of the Craftworlds who walks the Path of Command, a specialized path which studies all the different tactics a warhost of the Eldar Craftworld uses and then brings their different skills and abilities together into a single force that maximizes all their strengths and covers their individual weaknesses.
The Path of Command is the path that studies tactics, make plans and guides the Eldar in their war efforts. Those who walk it are referred to as Autarchs. Before becoming Autarchs, these Eldar would have studied in many of the different war temples of Khaine, mastering each path before choosing another. What this means is that Autarchs will have a range of varied skillsets and will be powerful warriors and great leaders.
On the board this allows you to select all manner of wargear to kit out your Autarch and create your own unique leader for your host. No two Autarchs need look alike and the modeling possibilities are endless.
They also make terrible decisions.
It should be noted that Autarchs are the favorite 'prey' of the Delfdar Succubi. Seeing as how the majority of Autarchs are drawn and portrayed as female and that Dark Eldar have a knack for torturing and raping their captives in intense BDSM sessions. One can only imagine....by the Emperor....
Prince Yriel of Craftworld Iyanden is perhaps the most famous of the Eldar Autarchs and is a swashbuckling Eldar pirate....in sphess! He beat up a bunch of nids though so he has some more balls than most Eldar. Interestingly, Yriel has never walked the Path of Command, but achieved his post of Autarch due to walking the Path of the Mariner.
Dawn of War 2
An Autarch appears in Dawn of War 2 called Kayleth from Alaitoc. She is known to be a complete bitch and an absolute whiner. She is That Guy if he had a vagayjay. Kayleth is also known for her dynamic entry which involves dropping several plasma grenades to soften up the enemy position before striking down the remains of whoever was dumb enough to get the hell out of ground zero. She is also a glass cannon, dishing out plenty of pain but cannot take the equivalent amount of damage in turn. She might be tsundere with Ronahn, but Ronahn's big/twin/younger sister Taldeer might contend with the relationship. She can also kill or, more likely, be killed by, Kaptin Bluddflagg.