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.
Now that we've located our root, we need its key signature to know which triad notes to 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.