Chord inversions are extremely important to piano players. You would be hard-pressed to find any piano music beyond the elementary levels that does not have inverted chords as a basic part of the fabric of the composition. Thus, every piano player needs to be confident and comfortable playing the inverted chords.
You can begin your learning and practicing of inversions very shortly after becoming familiar with all of the major and minor triads. Once you have them learned and mastered, learning how to invert the chords is the next step. At first, you should just go through the process of taking every chord you know through the 3 basic positions: root position, 1st inversion, & 2nd inversion.
After you have played each inversion, preferably with each hand separately & then with both hands, you can start trying to move from chord to chord. On the following video, I demonstrate every inversion of every major and minor triad for you in any easy-to-follow/easy-to-understand format. Then, I show you how to play through the inversions with both hands.
Watch the fingerings closely. Try to be consistent with the fingerings as you play through the inversions, as the fingerings can remain the same for every inversion on every triad.
Once you have become familiar with inverting chords, you will probably find that it becomes easier and easier. As this happens, you can consider taking on the exercise you see on the last part of the video. There you will see how to roll through your chord inversions, one note at a time, using the metronome to establish a steady rhythm and tempo. Gradually work your way up from slow tempos to fast.
Make these exercises a permanent part of your daily routine and you will be adding tremendous strength and understanding to your piano-playing foundation. Every advanced pianist has an extensive understanding of inversions and can play them without thinking. You can become an expert at playing them over time, and when you do, you will find them appearing all over the place. Inversions are an integral part of most piano music form the intermediate levels and up.
Without a doubt, pianists who have mastered inversions are going to have an easier time with music-reading, music learning and memorizing, and just about all that they want to do on the piano.
As usual, you can find a pretty extensive explanation of inversions at Wikipedia.