A chord is said to be inverted when its root is not in the bass (i.e., is not the lowest note). Any other chord-member may be placed on the bottom, the specific chord-member indicating which inversion it is.
For example, a "C-major" triad contains the three notes C - E - G. If the chord appears with the C in the bass, it is called "root position". If the E is in the bass, it is "1st inversion", and if the G is in the bass, it is "2nd inversion".
A chord may appear with any of its members as the lowest note, thus, since one position is called "root position", a chord with n notes has n-1 inversions.