In common parlance, "introverted" is basically synonymous to being shy, while being "extroverted" is the same as being outgoing. In terms of psychology, though, it's not that simple.
The way psychologists deduce whether you're intro- or extro-verted is with the question, "Where do you get your energy from?" A common example is a social party.
Introverts might not necessarily be the ones staying in the corner, not talking to anyone. They are, however, the ones who need to go home after the party, to "recharge". Being around people is draining. It sucks the energy out of introverts, who regain that energy by being alone for a while, getting that energy from within themselves.
On the other hand, extroverts draw energy from other people. A party is their charging station -- Friday nights are best spent outside because THAT'S their form of resting. Working on a project by themselves is tiring. So is dining by themselves, which is why they never seem to be by themselves.

People who are Sensing types are relatively more realistic than Intuition types. They gather information best through the five senses, and focus on what is actual and tangible. They generally like dealing with practical usages of what they learn.
On the other hand, Intuitive type people love reading between the lines. They're adept at inference and following abstract theories. Often, they have a difficult time trying to explain to Sensing types how they arrived at a conclusion, since their thought process is hard to track, and tends to make leaps and bounds, discarding things that are perceived to be "irrelevant".

Contrary to pseudo-psychology's claims, logical and emotional are not the two hemispheres of the brain. This preference has to do with how you make decisions.
Thinking types are more apt to use logic and reason to deduce which path to follow. They value the "cold" truth and fairness, and frequently nitpick about small inconsistencies.
However, Feeling types take a much more "people-friendly" approach to decisions. They care more about what's right than what's fair, and other people's feelings as opposed to always admitting the truth.

As opposed to its colloquial meaning, "Judging" in the Myers-Briggs sense doesn't hold a negative connotation. Judging types love making and keeping lists, and having things planned out beforehand. They're more task- and goal-oriented, and hate losing control of their life.
Perceiving types prefer to be more open to the possibilities, which sometimes sidetracks them and keeps them from meeting deadlines. They're relatively spontaneous, and respond better than Judging types to sudden changes in plans. From the opposing side, they can seem too casual, but it's this trait that allows them to still be productive while mixing work and play.