Haoshoku Haki is still a mystery. We have seen it used in different ways without an explanation to specify what it's power actually is.
So far we have seen it being used to:
-Knock people out (this is the most commonly seen use of this power)
performed by: Luffy,Shanks,Rayleigh,Doflamingo
-Nullify an explosion
performed by: Rayleigh
-Strike fear into opponents (Most commonly used on non-human beings. This is commonly believed to be the same as knocking people out but to less of an extreme)
Performed by: Shanks,Luffy,Rayleigh
From what I can tell because Rayleigh labelled Haoshoku Haki as the power of intimidation
Presence = Kenbunshoku HakiOriginally Posted by Silvers Rayleigh
Fighting Spirit = Busoshoku Haki
Intimidation = Haoshoku Haki
But how did Rayleigh nullify an explosion? Although it is unproven I believe he could have only done it using haki. How? Well to answer that intimidation doesn't have to be on living beings nor does it have to literally mean intimidating anything. It could be a nickname.
King/Conqueror signifies authority or "power"(not in terms of strength) and I believe that the power of a king surpasses all within their kingdom.
And therefore I believe the power of Haoshoku Haki is actually the rejection of phenomena occuring WITHIN living beings.
This includes Consciousness.
Phenomena is defined as:
(I know it's a bit broad and sketchy but we need to see more of the Haki)a fact, occurrence, or circumstance observed or observable: to study the phenomena of nature.