What is meant by the phrase "Allah does not intercede with anyone among His creation"?

The phrase is part of a hadith narrated by Abu Dawud and others, and its meaning is that Allah does not make an intercessor or a mediator for a creature. Intercession is mediating on behalf of another to bring about a benefit or avert harm. Allah is too great to be made an intercessor for some of His creatures. For this reason, the Prophet, peace and blessings be upon him, said: "Allah's majesty is greater than that."