"Kids these days..."[1]
Khaela Mensha Khaine is the Eldar God of War.
Official Canon
Khaine is an extremely powerful and angry War God that predates Khorne. He fought against the Necrons and the C'Tan, particularly The Nightbringer. Though he succeeded in breaking the C'Tan into many shards, the wound he received gave all Eldar the fear of death.
A prophecy from Isha's daughter Lileath foretold that the Eldar would kill Khaine; he decided that he would destroy the Eldar before they could kill him, but Asuryan intervened and placed a barrier between the Eldar and their gods. When Isha attempted to contact the Eldar regardless, he took her prisoner until Vaul promised to craft him 100 of his finest swords.
When Slaanesh was born, Khaine battled with the newborn god but found he couldn't overcome the Chaos God. Before he could be consumed, Khorne came to his defense and claimed Khaine as his own.
Regardless, Khaine's soul broke into pieces, each shard now being inherited by each craftworld. The Avatar of Khaine can be summoned in times of great need when an Exarch sacrifices himself to become the avatar's body. While quite powerful, the avatar lacks the god's full power.
The craftworld's Aspect Warriors are derived from different aspects of the War God, some inherited from his battle with The Nightbringer or given to him by Morai-Heg the crone.
TTS Canon
Khaine mostly appears in the Warpchat. He hates Slaanesh, and picks up Khorne for workouts at the gym.[1] Khaine will call all the chaos gods "kids" in comparison to himself, much to Khorne's annoyance.[2]