First Inversion refers to a chord whose root note has been raised by an octave so that it is no longer the lowest note in the chord, or the base note. The second note in the chord becomes the base note and the root note becomes the highest note in the chord.
In Second Inversion, the root note is raised an octave and the second note in the chord is also raised an octave.
The image displays the C Major triad in root position (C E G), first inversion (E G C), and second inversion (G C E).
The interval formula for a chord is changed when the chord is put in first or second inversion. The graphic below lists the interval formula for major, minor, augmented and diminished triads in root position, and when put in first or second inversion.
The interval formula for a major chord is major third, minor third. This equates to the third and fifth notes of the major scale on which it is built, or the pattern 1 3 5. The formula for a minor triad is minor third, major third. Another way to express this is the pattern 1 b3 5, which is also based on the major scale.
The different interval formulas that arise when a chord is inverted, means that the resultant sound has a different feel to the original.