An arpeggio is a way of playing a chord without playing all of the notes simultaneously, yet note by note.
This is a basic exercise of arpeggios in triad chords. In the video you can see the use of an arpeggio in a chord (including the octave note).
One example of this is the chord C. The notes that are played are C, E, G and also the next C note.
At the end of this video, the left hand is also used and plays the arpeggio with the right hand at the same time. This is a good exercise to coordinate the movement of your hands with each other.
This video is a simple chord progression using rhythmic runs or little variations at the end of the bar of each chord. If you know the chords and inversions well, you will be able to play a lot of variations and fills to give it a richer feeling and a sense of syncopation to the progression.
These fills in each chord can be made up with the notes that belong to each chord in any inversion, or with the notes that are part of the chord and with others that are not. Although, these notes must be part of the scale of the progression that is being played.
For example, in the chord E we can play notes like B, G#, F#, and D. Even though F# and D are not notes within the chord, they still belong to the scale that we are playing and they will sound good.
The important thing to know here about inversions and scales is that knowing scales does not necessarily mean that you will only be using them to play fast solos, but that they can be used for many other things.
In this video we see a basic exercise for basic jazz chords on the piano and also a scale. The chords that the pianist uses are Am7 – although he says Am9 in the video – and Bm7. These chords are repeated several times and then he adds CM7 chord (this is the chord that he says he doesn’t know what the name of it is). He plays a scale which he calls the D major scale without playing C#, but this actually would be G major scale, starting at the D note.
In music theory this scale would be called D mixolydian.
Although the terms that he uses in this video are not correct, this video is a good exercise for practicing jazz piano chords.