Well, let's say you take a major chord. It is build from the 1st (root), 3rd an 5th note of a major scale.
The chord root position is when the notes are played 1st, 3rd, 5th . In that order.
Simply put, a chord inversion is when you switch the order.
If you play 3rd, 5th, 1st , you've created what we call a 1st inversion. You basically take the 1st note and play it one octave higher.
The second inversion is when you play 5th, 3rd, 1st .
Since you always play the same notes, it is still the same chord but played in a different order. Chord inversions gives you more possibilities to play the same chord.
Here's a tutorial By Christopher explaining it in detail with examples :
http://www.guitartricks.com/lesson.php?input=9213&s_id=148
