What is a power of appointment?
In a common example, parents may leave their wealth in trust to a child, together with an unlimited power of appointment. The child draws benefits pursuant the trust during his lifetime and has the power to decide, in his own will, who will inherit his share of the trust when he dies.
Drafters of trusts governing large estates like to use powers of appointment when they trust the beneficiary (often their child) to decide who most deserves to receive the benefit of the trust years or decades into the future.
In Smith v. Ashford the Supreme Court interpreted a will in which the holder of a power of appointment sought to give the power itself to his wife. Without holding on the question of whether you can inherit a power of appointment itself (you can), the Court said that it didn't matter - the original power of appointment stated that it had to be exercised before its holder died. Since it was not so exercised, the power lapsed.