It's saying that each harmonic function is built up using different notes of the reference key, or tonic scale. Those are the notes that are used to build harmony that satisfies those functions. So, if you want to imply an harmonic function, or find the function of a set of notes, you'll be using those notes in some form and extent.
In other words, it's describing those three functions using pitches, notes. Each function is different, so it is described by different notes.
In the key of C we have:
1 2 3 4 5 6 7
C D E F G A B
That makes our tonic, or tonal center, or "home", to be C major. The subdominant is in the 4th scale degree, so F major, and the dominant is at the 5th scale degree, so G major. (For the chord qualities, we are just stacking thirds)
The tonic chord is C major, Cmaj7 chord is C E G B, which are the scale degrees 1, 3, 5, 7. Article mentions 1, 3, 5, 6, and 7.
The subdominant is F major, Fmaj7 chord is F A C E, which are the scale degrees 1, 3, 4, 6. Article mentions 1, 2, 3, 4, and 6.
The dominant is G major, G7 chord is G B D F, which are the scale degrees 2, 4, 5, 7. Article mentions 2, 4, 5, 6, and 7.
So, each harmonic function is characterized, described, achieved, by using those notes. Which makes sense, since they are built using mainly the diatonic chords of that scale degree (1 for tonic, 4 for subdominant, 5 for dominant).
On each function we are still missing one note, though: 6 for tonic, 2 for subdominant, 6 for dominant. According to the article, the 6 in tonic is an "associate", 2 in subdominant is an "associate", and 6 in dominant is a "dissonance". It also classifies all notes, but doesn't seem to explain exactly what it means by this categorization.