They used to date, although it seemed like it was Cobain the one who loved her, not her.
He had the "K records" logotype on his arm to delight her.
Cobain wrote most of the "Nevermind" songs about her. Some are very violent.
Songs like: "Lithium" (Cobain changed the lyrics after the split up because he wanted it to be about the relationship), "Drain You", "Lounge Act", etc.
Courtney Love said that he was "too fucking in love with her, that seemed stupid", and that she came in to show him his worth, but when Kurt reached famous life, Vail came back to him, but Love said to her: "Get out of here, bitch".