Chords are named after their root, or tonic note. Since there are 12 notes, there are 12 chords of any given flavor ... in other words, there are 12 major chords, 12 minor chords, 12 minor sevenths, etc., etc.
The two main shapes that are used to make barre chords are the E family and the A family. The other open chords we have learned (C, D and G) do not lend themselves to be barred ... they are too spread out for most hands/fingers to play them properly. However, if you have the hands for it, the C and G shapes can also move up and down as barre chords. I've always found it too uncomfortable, but I've seen many players using them.
Barre chords, or to use the less pretentious spelling, bar chords, are the reason the guitar is so cool. Simply put, all chord shapes can moved up and down the fret board, retaining their original quality—whether it's major, minor, major seventh, whatever—but changing pitch and name.
The index finger 'bars' the strings, in effect becoming the nut, while the other fingers form the familiar shapes 'behind' the index. While it's true that all chord shapes can move along the neck and retain their flavor, only a couple are really suited to becoming full barre chords.
The open chords we've looked at make use of some open-string some. Those notes are the result of the strings being stopped at the nut, which is the thick black line in the animation to the left. Here, you can see an E chord move up in pitch by two frets. The red line that appears is the barre (French for bar), which is done with the index finger; it acts in same way as the nut does in the open chord, which is to allow the notes on strings 1,2 and 6 to ring out. The important thing to understand is this: all the notes in the chord shape go up in pitch by the same interval (in this case a whole tone, or two frets) therefore the relationship between all the notes remains the same: that of a major chord. The open chord (E) and the new barre chord (F#) are both major chords. So, once you learn and remember the shape for any particular flavor of chord, you have in fact learned all 12 chords.
Playing barre chords will feel very uncomfortable at first and will no doubt sound pretty awful. Don't worry about it, you just need to desensitize the underneath of your index finger and get a feel for the pressure required to get a nice ringing sound, which will take a little time. On the following pages you can watch some videos of the main barre chord flavors moving up the fretboard. I have shown the most popular way of fingering them (in one case, the A form barre chord, shown two different ways), but some players prefer to curl their thumb over the edge of the fretboard to grab the bass note and form a mini-barre for the treble strings.
There are many ways to hold the notes down so you should feel free to experiment. The main thing is to remember the shapes so that you can either play the full chord with any finger configuration you choose, or use fragments of it. Your hand muscles will remember independently but don't let that muscle memory take over and be boss. You're the boss, not your fingers, and if you keep those shapes clear in your mind's eye, you can tell your fingers which bits and pieces you want to use ... eventually. And, eventually, you will begin to realize that all the notes defined by these shapes become great melody notes.