You may first see this creature at the end of the tutorial mission. Apparently the physical manifestation of the alien's psionic/data network, it is an electric yellow female-humanoid being, seemingly made entirely of electricity, save for a metallic skull and a bit of spinal column.
You will first fight it after you attempt to Skulljack a ADVENT Captain: you may want to make sure that Captain is otherwise the last enemy on the map. It has high health, a high dodge rate (so even point-blank shots may 'graze' it for partial damage), and high accuracy. It's abilities include teleportation (and can fire it's Plasma Rifle or use another ability after teleporting: a high-risk flanker), an AOE Rift-like attack that disables weapons for XCOM agents caught in it, then explodes at the end of your turn for significant damage if you leave a soldier in the effect. Sometimes after damaging it, it may also clone itself: the remaining HP will be divided between them, rounding down (so if it attempts to clone at 1 HP, it's basically a single teleport). For the storyline requirement, the best time to fight it is when there's no turn counter or anything keeping pressure on you.
Flashbangs and other causes of Disorientation greatly reduce it's threat, and seem to restrict it from using it's special abilities. After the first successful encounter, they will spawn in regular enemy pods, no longer in response to Skulljacking/Skullmining.
In terms of threat level, physical makeup, and plot significance: it is fairly equivalent to the Long War iteration of the Outsider.