You may wish to review Open Chords before continuing with this lesson.

Bar Chords (also known as Barre in French and Ceja in Spanish) are chords which use the first finger to depress two or more strings in the same fret.  Typically, Bar Chords use the shape of open chords farther up the neck with the first finger barring the fret where the nut would be relative to the shape of the chord.  For example,  if we take an E Major chord such as this:

E||-------|-------|-------|(open)
B||-------|-------|-------|(open)
G||---1---|-------|-------|
D||-------|---3---|-------|
A||-------|---2---|-------|
E||-------|-------|-------|(open)

and re-finger it with 2, 3, and 4 like this,

E||-------|-------|-------|(open)
B||-------|-------|-------|(open)
G||---2---|-------|-------|
D||-------|---3---|-------|
A||-------|---3---|-------|
E||-------|-------|-------|(open)

We can now take it up the neck as a Bar Chord. 
We know that E to F is a half step or one fret, so if we move each finger up one fret, we have raised the pitch of three out of six strings.  To raise the pitch of the open strings, bar the first finger across the entire first fret.  It is now F Major.  Because each note was raised exactly the same distance, the quality of the chord (Major) remains the same.  If we move the entire Bar Chord up a whole step or two frets, it now becomes G Major.

This particular example is known as the E Major form of the Bar Chord because it is based on an open E  Major
shape.  Any chord which requires three or fewer left hand fingers can be made into a Bar Chord, although some are easier to configure than others.