Open chords tend to sound "richer" than corresponding barre chords due to the fact that open strings resonate freely without any hindrance. An open chord is any chord that has one or more strings sounded without being fretted. Guitarists tend to use this name to refer to the chords that contain open strings that are played in the first position (first four frets).
Open Major Chords
Open Minor Chords
Open Seventh Chords
Chords in C major
Note that the chords in the key of C major consists of 3 major chords, 3 minor chords and 1 diminished chord. This holds true for all major keys.