An essential tone is a note that belongs to the harmony (chord) that’s played on top of that note. On the other hand notes that don’t belong to the underlying harmony is labelled as nonessential tones. Nonessential tones are also known as passing notes or auxiliary notes. When writing a chord progression for a melody, we should try to use chords that have the most number of essential notes in a given bar of the melody.
Let’s assume the first four notes of a melody are C F E and G. The chord that makes most sense to be played on top of this melody is the chord C which contains C-E-G notes. In this case the melody contains only one passing note which is F, which is also a consonant and a diatonic note in the key of C. So a C chord makes total sense and this is how we need to write chord progression for a given melody. We could even play all 4 notes to construct the chord which would be a ‘C add 11’ chord.
Sometimes more than one chord may make sense for the underlying melody and it is at the discretion of the composer to decide what chord to be used.