The 'Tonic' is whichever note is our root, and it represents the tonal center of a piece. A note that is diatonic means that it is one of the 7 notes of the major scale (or the minor scale if we're in a minor key)

Chromaticism

Let's take a look at the c major scale.

and now we'll compare it to the chromatic scale below.

The chromatic scale is all of the notes. When played in succession one right after the other, it doesn't exactly sound "good". It sounds utilitarian, but it can be another tool for us to add dissonance and tension to our melodies and chords.

Below we are applying this concept to our regular major scale.

We are moving chromatically from G to A. We can refer to this transitional note as an ascending passing tone. In the next example, we're moving downward, so we'll notate the passing tone as A♭, since we're moving from A to G this time.

The use of an accidental indicates our melody is not diatonic to the scale.

The Tonic

To wrap our minds around chromaticism, we need to understand how applying standard music theory works when analyzing a piece of music. Everything is based off of the major scale. So instead of using note letters, we can usually describe music just using numbers.

A standard convention is to list chords by their root's scale degree. Simply saying 2 - 5 - 1 in the key of C indicates we want a chord progression that builds diatonic chords on the 2nd degree, 5th degree, and root (1st degree) of the C major scale. Generally, in a jazz context, this can imply either triads or seventh chords.

When describing music from any tonal center, it's common to use roman numerals to represent the chord. The tonic is the I. Our I chord above is a C maj7.

If we wanted to construct our progression in the key of A, we'd get the following chords instead:

In the above example, the tonic is our A maj7 chord. The 2 - 5 - 1, or II - V - I, is a progression that utilizes intervals of a 5th to transition. Moving by 5ths is a solid technique to logically transition between different sections of a scale.

The 'one' is a musical concept that represents our tonal center. It simultaneously refers to the root of the key you're in (the 1st degree of the scale), and the chords that can be built on top of it - I maj / I maj7, and if you're in a minor key, i min / i min7.

Diatonic

It's fairly easy to see when a score has non-diatonic notes. We can take our D min7, G 7, C maj7 example and alter the dominant chord with a tritone substitution, a common technique for adding chromaticism to a standard progression.

In the above example we've switched G 7 for D♭ 7. These chords both share B (C♭) and F, the tritone (augmented 4th / diminished 5th) that gives the V 7 chord it's dominant nature. When we have a V 7 chord, or any dominant chord, we can usually switch it out for another dominant a tritone away. In a standard II - V - I progression, the substituted V 7 chord happens to be a half step above our target I chord. This creates chromatic movement in the bass line.

As you can see, this alteration causes us to use accidentals in this phrase. Seeing accidentals being used to alter the key signature (in this case C Major) is an indicator that we are no longer sticking to diatonic notes in the piece. Below is one last look in the key of E.

II - V - I in E (diatonic to the E Major Scale)

II - subV - I in E (uses a tritone sub/chromatic bass movement)