The importance of knowing and understanding the harmonized major scale is vital to any musicians ability to communicate something melodic when soloing over a chord progression or in composing music that makes sense.

What is the Harmonized Scale?
Most people who had some kind of basic music in grade school are familiar with the sound of the do, re, me, fa, sol, la, ti, do construction of the major scale. Those individual notes are built on a series of whole steps and half steps. If a person were looking at a piano keyboard and located the note C, he would notice that it was a white key. The very next key would be a black key a half step away, followed by another white key then another black key. Each step from one key to the next is called a half step. To go from one C note to the next C note would require 12 steps known as the Chromatic Scale. There are two places where a white key is followed by another white key. The notes E to F, and the notes B to C. If a person wanted to play a C major scale, he could play all the white keys starting on C, and the construction would be; whole step, whole step, half step, whole step, whole step, whole step, half step. That would be 7 notes ( no black keys ) with the 8th note being the starting point of C once again and bringing the player to the next octave.

A person could take every other note and play them together and arrive at the chords that would be diatonic to the family of whatever key he was playing in. For example, in the key of C, one could play the C, E, and G, and he would have a root position C major triad. Following that same formula, he could then play every other note starting on the 2nd note, D, and play D, F, and A which would give him a D minor triad. Applying this same formula with each successive note will present the scale in harmony.

Breaking this down it would look like this:

Major triad - C E G
minor triad - D F A
minor triad - E G B
Major triad - F A C
Major triad - G B D
minor triad - A C E
diminished - B D F

These are the fundamental building blocks of chord construction. It is how chords are built. All chords are derived from the major scale. Those chords can be altered in a variety of ways by adding additional notes called tensions, or "color tones". Those are the salt and pepper notes that make things interesting. Sometime notes that are not diatonic to the key can be added to stretch the harmony even further. Ones own ears are the final judge when it comes to what works and what doesn't.

Sources
Berklee College of Music.