A hypothetical person who, as dictated by his nature and essence, is logically capable of performing only one action: scratching his ear.
This character was proposed as a device for refuting a certain definition of omnipotence suggested by Edward Wierenga, which goes roughly like this: A person P is omnipotent at time T IFF P can actualize any state of events S at time T, such that actualizing S is logically consistent with events prior to T. In other words, you're omnipotent if you can do anything which it is logically possible for you to do. Under such a definition, McEar would be considered omnipotent.
Wierenga attempted to counter this objection by arguing that McEar isn't possible -- scratching one's ear involves a number of other actions, including moving one's arm. But the point of the McEar objection is the vast number of things that McEar is not able to do. The point is that, under Wierenga's definition, McEar would still be omnipotent.