Insanity is a spectrum of behaviors characterized by certain mental or behavioral patterns. The entire story of My Immortal could be considered insanity in and of itself (but for the sake of my sanity and your own, I will not go into too much detail about it). One can characterize insanity as displaying behavior outside of the socially accepted norm, to the point of discomfort or harm to oneself or others around oneself.
Ebony is a prime example of insanity, as Tara often makes her perform acts of self-harm in her story. Acts of insanity/self-harm are performed by many other characters, such as Vampire, B'loody Mary, and Draco. Arguably, every character in the masterpiece "My Immortal" is insane. Tara's habit of changing characters and flinging characters into the story often causes the story to be dropped into a pit of insanity-poisoned spikes and left to die. Of course, with Tara's writing style, it would not be surprising if the story came back to life a chapter later, only to never be mentioned again except in offhand situations.
Insanity is one of the main entertainment points of the story, as it has absolutely no reading value (aside from showing readers what vomit put into words on an electronic page looks like) otherwise. It is not incorrect for one to presume that without the insane aspect of "My Immortal", the readers would have gouged out their eyes and tossed them into an open flame. Of course, this act would be considered insane as well.
Tara herself may also be insane, as she and her characters share so many qualities that they are sometimes indistinguishable; Tara often accidentally replaces Enoby's name with her own in some way or another (see Ebony's alternative names). She is often assumed to take interest in self-harming actions such as slitting her wrists, just the same as Enoby.
For the purpose of the story, insanity is mainly when a character decides to perform an action of self-harm.
Now if you'll excuse me, due to having just read this story, I must now go and be insane momentarily.