Gain Haunt Escalation and Haunt Deescalation.
You are spiritually tied to a specific object, place, person or deed and have some "unresolved business" involving this. Until this business is "resolved", you cannot be truly killed. Instead of dying, you escalate, dissipating into a spectral mist and remanifesting as a more threatening being at the point your haunting originates from.
It is also possible for you to be "solved" if someone addresses whatever it is that is causing you to haunt. This typically involves making you come to terms with something and could be as simple as convincing you that you are dead and telling you how it happened. But it could also be providing some sort of justice or revenge or something much more arcane. The details differ from haunt to haunt, but there are often hints in the haunt's behavior and surroundings.
If a creature makes progress towards solving you, that reflects in your behavior. You may be less aggressive towards them, appear to be listening to what they say, or even deescalate.
You remanifest at the start of your next turn as an angrier and more powerful undead being, lashing out at whatever killed you as well as anything else in your way. This resets all HP, MP, and temporary effects that may be present on you. Every time you escalate, you move one step forward on the following track. For instance, if you were already a phantom, you would escalate into being a specter.
Most haunts do not escalate past wraith. But the GM may rule that certain especially angry or powerful ones have additional abilities or escalation steps. If you escalate while already fully escalated, you do not change species or gain additional abilities, but you still become more aggressive, harder to solve, and reset all HP, MP, and temporary effects.