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 chords refers to the way a chord is constructed, by including open strings. But, since its most useful area is to describe a chord that is not a barre chord, an chord without open strings could still be called open. Since there are none accurate term to otherwise describe a chord such Cm7 on the picture above (closed chord as a term in this case is somewhat problematic) all chords that don't are barre chord could be called open chords.
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 chords is that some chords have 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 cases have no natural fingerings in the standard tuning and because of that 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?