The core of this movement is pretty simple to understand. A Diminished chord is built by stacking minor thirds.
Lets take this diminished chord, and outline it melodically, by putting each note on a downbeat:
Now here's where the triplet comes in. When you play a chromatic scale, it takes 3 notes for you to move by a minor 3rd, the same distance between each of these diminished notes.
So, by moving up or down the chromatic scale in triplets, we will land with the diminished chord notes on the beat:
So, why is this useful? Because, anywhere you play a diminished chord, you can use this triplet as a movement in and out of that chord.
For example, lets say we sere using this D diminished chord as a voicing for G7b9. (Note, the Cb in D dim is the same as B, the 3rd of G7). You could use this idea as a drop-2 movement on G7 to Cmaj like this: