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.