What Jung talks here about the unconscious function could be referred as the shadow function:

Quote Originally Posted by Jung; psychological types
Besides this general function(dominant), the unconscious also possesses functions that can become conscious under other conditions. The thinking type, for instance, must necessarily repress and exclude feeling as far as possible, since nothing disturbs thinking so much as feeling, and the feeling type represses thinking, since nothing is more injurious to feeling than thinking. Repressed functions lapse into the unconscious. Just as only one of the four sons of Horus had a human head, so as a rule only one of the four basic functions is fully conscious and differentiated enough to be freely manipulable by the will, the others remaining partially or wholly unconscious, This "unconsciousness" does not mean that a thinking type, for this instance, is not conscious of his feelings. He knows his feelings very well, in so far as he is capable of introspection, but he denies them any validity and declares they have no influence over him. They therefore come upon him against his will, and being spontaneous and autonomous, they finally appropriate to themselves the validity which his consciousness denies them. They are activated by unconscious stimulation, and form indeed a sort of counterpersonality whose existence can be established only by analyzing the products of the unconscious.
When a function is not at one's disposal, when it is felt as something that disturbs the differentiated function, suddenly appearing and then vanishing again fitfully, when it has an obsessive character, or remains obstinately in hiding when most needed--it then has all the qualities of a quasi-unconscious function. Other peculiarities may be noted: there is always something inauthentic about it, as it contains elements that do not properly belong to it. Thus the unconscious feeling of the thinking type are not singularly fantastic nature, often in grotesque contrast to the excessively rationalistic intellectualism of his conscious attitude. His conscious thinking is purposive and controlled, but his feeling is impulsive, uncontrolled, moody, irrational, primitive, and just as archaic as the feelings of a savage.
The same is true for every function that is repressed into the unconscious. It remains fused together with elements not properly belonging to it, in a archaic condition--for the unconscious is the residue of unconquered nature in us, just as it is also the matrix of our unborn future. The unconscious functions are always seminal ones, so it is no wonder that sometime in the course of life the need will be felt to supplement and alter the conscious attitude.