Piano and other keyboard instruments such as organ, synthesizers, harpsichord, and guitar are pre-eminently harmonic instruments. Piano sums up an orchestra potentialities. A pianist has 88 notes at his disposal, nearly all those a human ear can hear. Moreover, he uses two hands and ten fingers.
These are obvious, banal considerations but they underline piano rhythmical and above all harmonic potentialities. In theory, a pianist can play 10 notes at the same time. However are not usually used more than 7or 8 notes simultaneously because of harmonic laws (chords).
A pianist's left hand often plays chords to accompany the right hand or the rest of the group in which it plays. In jazz, blues, funky, pop and other musical genres a pianist plays chords with the left hand and improvises with the right one. I introduce the jazz voicings or the main positions used during the improvisation or the jazz, blues, pop, pianist accompaniment.
In piano solo concerts, the pianist often plays chords with his right hand both in accompaniment both in improvisation. It happens in a different way if compared with left hand, considering the situation on which it plays. For example, in a jazz song accompaniment, the pianist plays a classical voicing in three or four notes with the left hand and an octave with a middle note triad chord with his right hand, that is the 9th , the 5th and 9th, a higher octave again. Do not worry if you do not understand anything. While reading it will be clearer.
This section is very important. I explain here how to play a non-classical song in solo piano. Moreover, these techniques are useful to improvise with the piano. For example, I explain how to harmonize a melody with the right hand.