Jungian functions usually refer to the eight different mental processes Carl Jung described in his work Psychological Types. These functions, or "psychological types" as they may be, fit into the bigger scheme of Jung's view on human nature (see Jungian Constructs for a good description of this). Although Jung's typology is speculative and was not developed using scientific methods per se, it seems to be both comprehensive and sensible.
Jung was very dialectic - he divided most aspects of human nature up into opposing pairs (light-dark, ego-shadow, yin-yang, etc.); much unlike Sigmund Freud, who seemed to like trinity (oral, anal phallic; ego, superego, id). Also unlike Freud, Jung believed that there were inborn differences in human nature that could not be justified as simply "products of the environment." He was more on the nature end of the nurture vs. nature debate, and his typological functions bear witness to this.
Long before he had come up with the functions themselves, Jung had speculated that every person had one of two opposing attitudes - they were either Extroverted or Introverted. The designation "Extroverted" denotes high-energy people who draw their energy from the surrounding environment: from outside themselves. Introverts, by contrast, are far more low-energy; and they get what energy they do have from within their selves. Thus, where the one places emphasis on action in the external world, the other is given to internal reflection.
Although Jung thought extrovert vs. introvert was the most important factor in shaping one's personality, people who've expounded on his work more recently tend to disagree. Modern neuroscience seems to indicate that extroverts rely more heavily on the frontal portions of the brain (where dopamine is produced); while introverts' brain functions are closer to the posterior (the more reflective part).
Deriving the Functions
As Jung's view of the Self became more sophisticated, so did his typology. The extrovert-introvert dichotomy was only the beginning. But as he fleshed out the rest of his typology, Jung continued to use the yin-yang, dialectic method.
Perhaps the first thing Jung noted was that there were two overall functions (super-functions, if you will) a person's mind will perform. A person will gather information (Perception), and they will make assessments based on that information (Judgement).
But what about this Perception - this gathering of information? Does everybody perceive things in the same way? No, said Jung, there are (surprise!) two opposing ways a person might go about gathering information. Some people perceive reality in a very concrete fashion. Reality is reality, A is A, just as we perceive it through the five senses. This method (function) of perception is called Sensation. Sensate people are very concrete - they are very down to earth, seeing reality for just what it is.
On the other hand, some absorb information in a much more abstract way. These folks do not perceive things in terms of concrete objects; rather, they connect everything to ideas, concepts, and symbols of various sorts. This function is called Intuition. Unlike Sensates, Intuitive people see things in broad, general terms (big picture), and are more inclined toward displacement - their thoughts will tend toward that which is not at hand, past & future, the abstract.
So, according to Jung, everyone must perceive things somehow. In doing this, one will have a natural preference to either do it concretely (Sensation), or abstractly (Intuition).
As stated above, Jung also noted that people act & react (judge things, in other words), based on what they perceive. This judgement might also take two forms. On the one hand, a person might make decisions in a very objective way. In evaluating information, these sort of folks use firm, impersonal methods - logic, principles, philosophy. This is very characteristic of the Thinking function. Those with a preference for Thinking tend to act on the basis of reason, not so much on the basis of emotion. However, it would be a mistake to say that Thinkers do not have strong emotions - they are simply more apt to put those emotions aside when it comes to decision-making.
In contrast, there are also people who prefer subjective means of judgement. A person whose ethic is based largely on values, who must sort through all their emotions before acting, would fall into this category - the Feeling function. Emotions and subjective concerns (the animate world) are likely to preoccupy the mental landscape of a Feeler. Those with the Feeling preference will often be more focused on the emotions; and thus may be seen as more personable or friendlier. On the other hand, immature Feelers might also be whiny or dependent.
Thus, we have the four overall functions:
Individual Conscious / \Intuition
& Unconscious ----
However, we must not forget that each of the four overall functions will have an attitude - it will either be Extroverted or Introverted. This is a rather important difference, since (for example) Extroverted Feeling and Introverted Feeling behave in completely different ways...modern neuroscience suggests that they're located in opposite quadrants of the brain. The combination of two attitudes (Extroverted, Introverted), and four functions (Sensation, Intuition, Thinking, and Feeling) gives us a grand total of eight Jungian functions.
Jung's theory suggests that each individual is dominant in one of these eight functions, and their personality will thus reflect that function's attributes. The eight functions, with a very cursory description of each function's attributes, is as follows:
Extroverted Sensing (abbreviated as Se) - Absorbs reality in a very active way, using the concrete senses. Commonly type-cast as being a thrill seeker.
Extroverted Intuition (abbreviated as Ne) - Perceives abstract connections within the external environment; views things in a global fashion.
Introverted Sensing (abbreviated as Si) - Very methodical: notes and remembers information & sensory details.
Introverted Intuition (abbreviated as Ni) - Abstract, yet linear. Perceives internal patterns; projects these patterns into the future. Rather mystical, especially when in conjunction (junction) with a Feeling function.
Extroverted Thinking (abbreviated as Te) - Makes and acts upon external decisions based on objective principles. Decisive and confident.
Extroverted Feeling (abbreviated as Fe) - Uses subjective values & emotions to make outward decisions...Judgement process is cognizant of societal/cultural values.
Introverted Thinking (abbreviated as Ti) - Reflectively evaluates things in a logical fashion; seeks coherence. Spatial and form-oriented...Incidentally, Carl Jung himself was a dominant Introverted Thinker.
Introverted Feeling (abbreviated as Fi) - Also spatial and form-oriented, but the inward evaluation is a subjective, emotionally-reflective valuing process. Seeks harmony.
So which of these functions is my dominant one? Well, if it were Extroverted Sensation, I'd have probably bored myself to death by writing such a long & dry node. If it were Extroverted Thinking or Extroverted Feeling, my priorities would be more in order, and writing this node wouldn't be one of them. If it were Introverted Sensation, I'd have no patience for such an abstract subject; and if it were Introverted Intuition, I'd be fascinated by the subject - but I'd be wiser, so I'd realise how futile the endeavour was. So I guess that leaves Introverted Judgement (of which I'm pretty evenly balanced between thinking and feeling). Course, I didn't address Extroverted Intuition, but that's my auxiliary (next-best) function, so it all works out okay.
Jung's Typology fleshed out further by Myers & Briggs
Jung's functional typology was interpreted and popularised by Isabel Myers and Katherine Briggs. Each of the Myers-Briggs (MBTI) types is connected with a Jungian function according to the following rule: for extroverted types, the dominant function is the preferred judging function (thinking or feeling) if the individual has a "Judging" preference as the fourth letter of their Myers-Briggs type; but is the preferred perceiving function (sensing or intuition) if the individual has a preference for "Perceiving" as such. Thus, an ESTJ would have dominant Extroverted Thinking, as the "J" preference indicates that their dominant function will one of the two judging functions, of which this individual has a "T(hinking)" preference.
The reverse is true for introverted types: an introvert's dominant function will be a judging function if the introvert has a preference for "Perceiving," whereas their dominant function will be a perceiving function if the introvert has a preference for judging. Thus, an INFP would have dominant Introverted Feeling, for the "P" indicates a dominant judging function among introverts, and this individual has an "F(eeling)" preference. In the end, it pans out as follows:
Extroverted Sensing types: ESTP and ESFP
Introverted Sensing types: ISTJ and ISFJ
Extroverted Intuitive types: ENTP and ENFP
Introverted Intuitive types: INTJ and INFJ
Extroverted Thinking types: ESTJ and ENTJ
Introverted Thinking types: ISTP and INTP
Extroverted Feeling types: ESFJ and ENFJ
Introverted Feeling types: ISFP and INFP