The basis of harmony in Western music is the triadic chord, a three-note harmony performed to be heard simultaneously.  While endless other chord tones, extensions and alterations can be incorporated into a triad, ultimately, their defining structure is the triad from which any more complex chord is derived.  The two most common triads, major and minor, are derived from their eponymous scale structure by selecting the first, third and fifth note of their respective scales.  For instance a C major triad is extracted from a C major scale like so:

C major    C          D          E          F           G        A         B         C

Interval     R         M2        M3       P4         P5      M6       M7      P8

This results in the pitches of the C major triad: C, E, and G.  Regardless of how these three notes are arranged, they always result in a C major triad.  All of the following chords are C major triads:

Inversions

That triads can arrange their pitches in any configuration brings us to our next topic: inversions.  The lowest pitch in any harmony is called the “bass” and the highest is called the “soprano.”  When the root of a chord is the bass, it is referred to as being in “root position.”  The first, second, and fifth shapes in the diagrams above are in root position.  We notate a chord in root position simply by writing the name of the chord, in this case “C”.  Note that a chord with no specified quality is assumed to be a major triad.

When we “invert” a chord, we move the bass note up an octave or more, resulting in the next highest chord tone being in the bass.  Inverting a root position major chord results in the major third being in the bass.  This chord is referred to as being in “first inversion.”  Any time the third of a chord is the bass, it is in first inversion, regardless of the configuration of the chord tones above it.  An inversion is notated in contemporary music by writing the the name of the chord followed by a slash and the chord tone in the bass.  Therefore, a first inversion C major triad is notated as C/E (pronounced “C over E”).  As you can see, the third shape above is in first inversion.

A triad in first inversion can be inverted a second time to produce a second inversion triad.  With a major triad, this means moving the major third up an octave or more, leaving the perfect fifth in the bass.  Any time the fifth of a chord is in the bass, it is in second inversion, regardless of the configuration of the chord tones above it.  A chord in second inversion is notated using the same method as a first inversion triad. Therefore a C major triad in first inversion is notated as a C/G.  As you can see, the fourth and sixth shapes depicted above are in second inversion.

Using Inversions

Inversions have a number of uses.  One of the most common is creating smooth bass motion.  Example 1 below has simple chord G-D-Em chord progression.  Notice how the lowest note in each chord (the bass note) leaps dramatically between chords.  By placing the D in first inversion, the bass motion becomes stepwise, “walking down” from G to Em. 

Another use for triad inversion is voice leading, the creation of smooth movement from one voicing to the next.  Jumping from chord to chord in root position causes large leaps in some progressions, which can be jarring to the ear  A chord progression is said to be voice led when all pitches from one chord move to the next chord by an interval no greater than a minor third.  In Example 2, the G-C-D-G progression moves by large leaps from G to C and D to G.  By incorporating inversions, the motion between chords becomes smooth and remains in the same fretboard position. 

It is important to consider that when playing in a full band the guitar player does not decided what pitch is in the bass.  That is decided by whomever is playing the lowest pitch, most often the bass player.  This is very useful to the guitar player, as it frees them up to play whatever voicing best suits their needs.  They can voice lead the triads or leap between voicings for effect.