Inversion
An inversion is a chord voiced with a note other than its root at the bottom. Most chords are stacks of thirds with the root in the bass; rearrange them so a different chord tone is lowest, and you have an inversion. The chord is still the same chord - the same notes, the same name - it just has a different note underneath.
Triad inversions
A triad has three notes, so besides root position it has two inversions. Take C major (C-E-G):
- Root position - C in the bass: C-E-G.
- First inversion - the third in the bass: E-G-C.
- Second inversion - the fifth in the bass: G-C-E.
A four-note seventh chord has three inversions (third, fifth or seventh in the bass), and so on as you add notes. Inversions are commonly written as slash chords: C major with E in the bass is "C/E", read as "C over E".
Why bother
The main reason musicians invert chords is voice leading - keeping the movement from one chord to the next smooth, so individual notes shift by small steps rather than leaping around. Inversion changes the bass line and the texture without changing the harmony, which makes progressions flow. How the notes are spread out more generally is a chord's voicing.