Essence of The Revelation principle in Mechanism Design

Consider a group of people with individual states (say, willingness to pay for a good in an auction).

Give a mechanism for aggregating claims about those states (possibly false) and spitting out an allocation (for instance, “you may bid in a first-price sealed-bid auction”).

Then any allocation which can be reached in some mechanism can also be reached in a truthful mechanism, a mechanism where each person has no incentive to lie about their state