A more thorough explanation:

A discretionary power of appointment is a type of power that is not mandatory to exercise. The person who has the power can choose whether or not to use it. The power is valid as long as there is at least one person who fits the description of the class that the power can be exercised in favor of (the objects of the power).

If the person with the power of appointment (the donee) decides to use the discretionary power, they must do so intelligently and in line with the decedent's purpose. The exercise of discretionary power can be either exclusive or non-exclusive.

For example, let's say a wealthy individual creates a trust for their grandchildren. The trust document gives the trustee the power to distribute the trust assets to the grandchildren as they see fit. This is a discretionary power of appointment because the trustee can choose whether or not to distribute the assets to the grandchildren.

Another example is if a person creates a will that gives their spouse the power to distribute their assets to their children as they see fit. This is also a discretionary power of appointment because the spouse can choose whether or not to distribute the assets to the children.

These examples illustrate the definition of discretionary power of appointment because in both cases, the person with the power can choose whether or not to exercise it. They must do so intelligently and in line with the decedent's purpose.