A root of the chord is the bottom note in the chord after which the chord is named. (Example: in the chord A major, the root note is A)
A chord inversion is when you put the next node from the triad (Root - 3rd - 5th) on the bottom
A "1st Inversion" is when you put the 3rd on the bottom of the chord, instead of the Root
A "2nd Inversion" is when you put the 5th on the bottom of the chord, instead of the Root
Play the chords from the diagrams below. You can see that the sound is slightly different from Root to 1st inversion to 2nd inversion, however the nature of the chord remains the same.
Chord inversions are more popular in piano than guitar, because they are easier to play with two hands. On guitar, however, knowing these shapes will give you extra harmonic options when playing chords
Experiment playing the chord progressions you already know by using 1st and 2nd inversions instead, and note the sound difference. You can also throw in an occasional inverted chord here and there for variety's sake
The below examples are only for major and minor chords, but you can come up with inversions for all kinds of chords, such as dominant and extended chords. Also you can add extensions on top of inverted chords
In the below examples you can see that the chord on the left always has the Root note on the bottom. The chord in the centre has the major or minor 3rd on the bottom. And the chord on the right always has the 5th on the bottom.