A direct mind-computer interface is literally that - a direct cybernetic link between a mind and a computer. For purposes of this term, the word 'mind' is usually understood to imply the conciousness of an organic life form and 'computer' is usually understood to imply an inorganic processing device of some type. The term 'direct' implies that the exchange of data between the mind and the computer is not handled through intermediate organs such as the eyes, ears, mouth, or hands (currently the most common sets of organs used to interface one's consciousness with a computer).
These semantical notations are crucial in the contemplation of a direct mind-computer interface, as depending on one's point of view as to what the term 'mind' and 'computer' mean, a direct mind-computer interface may fall under various catagories from "already extant" to "possible but not currently in existence" to "completely impossible." For example, if an individual believed that the 'mind' was an ineffable construct, with no direct link to any physical construct that we can detect, then demonstrating to that individual an electronic coupling between the brain of an animal (of whatever order), and an electronic device would not be a compelling argument.
From a standpoint of pure fact, direct mind-computer interfaces can be said to already exist. There have been many tests in the field of linking an animal's or a human's brain cyberneticly to an electronic computing device. From monkeys hardwired into robotic armatures to a blind man that has had CCD chips and neural implants installed which allow him to see, albiet at a very low mono-chromatic resolution.
The current state of the art can be more accurately described as a direct brain-computer interface. The distinguishing point being that the mind or consciousness is completely seated in the organic brain and there is a sharing of impulses that sends data between a brain and an electronic device.
A true direct mind-computer interface implies that full integration between the concious entity, and a computational device. Such a linking might allow for a consciousness which is an emergent property of an organism's brain to migrate into an inorganic device holisticly. It may entail simply expanding or enhancing the existing concsciousness.