In a Major Scale, use every other note up to the 5th note, and you have a triad:
Every other note from start to fifth, is:
This forms a triad. These three notes sound pleasant when played together, because they're all in the key of D Major.
Why do we need Triads? They form a basic Chord. Improvisation flows over chords changing keys.
Therefore, to improvise a melody, we must know our Key (which notes to sharp or flat). First, we find our Chord's root, called Tonic, or the 1st note of a scale.
Within a song, a chord's root is one note to which every other note revolves around, or resolves to, in sound. Play or sing some notes you hear in a particular chord. Then play up or down its key's scale, to reach the bottom or top root note.
Locating the Root, we build a triad from it. We need the Root's Key signature (which notes are sharp or flat).
If the root note is E, then E Major is a Key with sharps. Using the sharps rule:
First, move E down a half step, to D#. Second, with the Order of Sharps, count up to D# :
FCGD notes are sharp now.
Use these sharps in the E Major Scale alphabet, with E as Root:
Now, let's make our Triad: Every other note up to the Fifth (5th) note is:
That makes the E triad.
For a simpler method, count every other note in the E scale:
Then, find the Key Signature for the correct Sharp notes in the E Major triad:
Additionally, Triads help us to play a solo, or improvise, since we need a reference for the patterns we play. The anchors of first, third, or fifth notes marks our location in a scale.
Triads give a melodic structure, inspiring other scale types, key change prediction, and arpeggio (note pattern) creation.
Finally, Triads are both shortcuts to remember a Key, and also chords that change within a song.
Recommended reading: More about Triads
The next page is about modes that alter notes to modify a key's sound.