Inversions are ways of playing the same chord to either give you a different top note, complete sequence or just allow you to move your fingers less. It is just playing a chord in a different way. In classical harmony you'd have the original chord and two inversions, as follows:
Using C as an example:
Take D minor 9 - D F A C E
N.B the below chords work on the premise your left hand is playing the 'D', or it's being covered by a bass player or some other low-end instrument.
These really come into play when using them in a chord sequence. This means you'll have a more 'solid' sounding sequence and you don't have to re-finger 4 or 5 note chords each beat.
We're going to use a simple ii V I [minor 2, dominant 5, major 1.] in C, which is Dm, G7, Cmaj. Concentrating on two of the above voicings:
LH | RH | chord |
D | F A C E | Dm9 |
G | F A B E | G13 |
C | E G B D | Cmaj9 |
LH | RH | chord |
D | C E F A | Dm9 |
G | B E F A | G13 |
C | B D E G | Cmaj9 |
In both instance I've highlighted which fingers would move changing between those chords.