The most common chords often used by so-called singer-songwriters are the open chords. These chords are, however, common in lot’s of styles. They are known as open chords because some of the strings are played without a finger placed on them.
Open chord referring to the way a chord is constructed, not to a specific chord. An open chord can be a C or it can be a C7 or it can be a Cadd9. You can often play a certain chord as both a barre or as an open chord, the difference is the sound (and the shape of course).
The open chords suits very well on an acoustic guitar or electric guitar with clean sound from the amplifier. The tones rings out well and it has a pleasant crispy sound.
The drawback with open chord is that some chord has quite difficult fingerings. Above you can choose from notes C - D - E - F - G - A - B whereas C# (or Db), D#, F#, G# and A# are missing. This is because these chords in many times have no natural fingerings in the standard tuning and therefore often is played as barre chords or with a capo.
Chord note structure
Here's information about which notes each chord consists of. Note that you sometimes are strumming more strings than the numbers of the notes of the chord you are playing, this is because some notes are duplicated, but in different octaves.
C: C – E – G
Cm: C – Eb – G
Cmaj7: C – E – G – B
Cm7: C – Eb – G – Bb
C7: C – E – G – Bb
C6: C – E – G – A
Cm6: C – Eb – G – A
If you want to know more about the theory for each of the chords, read What is a chord?