A re-arrangement of a major, minor, dimished, augmented, or any other chord. When dealing with triads, there are 3 ways to arrange the notes ( 1 root position, and 2 inversions ). For our example, we shall use a C major chord.

            1st 2nd inversions
           Root  \/  \/
-----------------------|
                     E |
-----------------------|
                 C   C |
-----------------------|
                       |
-----------G-----G---G-|  - V (Fifth degree)
                       |
-----------E-----E-----|  - III (Third degree)

-----------C---------     - I (Root Note)
This is the first, or root, position of the chord. A first inversion would move the root to the top of the chord, like so:
C
G
E

A second inversion would move the third and the root up an octave:
E
C
G

Now, replace the root, third, and fifth with their equivalent members of other scales (dim, aug, etc). 'Hoo ray' for inversions!