In reality, any combination of 2 or more tones is a chord.  However, many tone intervals are discordant  - meaning they are not pleasing to the ear.  The chords we use most often tend to be groups of notes that yield a pleasant combination.

It can be very confusing on a guitar because not all chords are formed with the Root note as the lowest note in the chord.  Sometimes, the chords are somewhat inverted and may also double certain tones.  Alternative versions of the same chord simply voice the chord with a different combination of the same tones.

All major chords have the same pattern of intervals.  Likewise, all minor chords have the same interval patterns.  Major chords are based on the major triad (3 tones) and minor chords are  based on the minor triad.

A major triad is Root, Major Third, Fifth.  Another way of describing this is in terms of semi-tones (1 fret = 1 semi-tone = 1 half-step).  In terms of semi-tones, the major triad is Root, +4, +7.

A minor triad is Root, Minor Third, Fifth.  In semi-tones that is Root, +3, +7.

Seventh chords simply pile on a forth tone to the basic major or minor triad.  A Major 7th uses the basic major triad and adds one tone that is the 7th tone in the scale.  In terms of semi-tones a Major 7th would be Root, +4, +7, +11.  This extra tone is just one half step below the root's octave - consequently, Major 7th chords have a 'shimmery' and almost discordant feel. 

Minor 7th chords are built on the minor triad and also just add that forth tone which is +11 semi-tones up the scale.

Another (and more common) type of 7th chord is the Dominant 7th or V7 or Five7.  If you are playing in the key of C, the V7 chord is G7.  A V7 chord has a major triad plus a note that is a flatted 7th above the root (+10 semitones).  These V7 chords are very useful as leading chords helping to resolve back to the key's I chord.

Do you have understand all this in order to play and have fun?  No - but the more you understand the structure of music, the better musician you will become.  Like Jerome says - it's all about scales.

This is way too long of a response . . . sorry.  But - here is a very useful gizmo in Wikipedia that helps demonstrate the structure of chords.  This chord building grid this is way cool - I don't know who dreamed it up, but it is absolutely brilliant:
http://en.wikipedia.org/wiki/Chord_building_grid