Have you ever listened to a major chord? I mean, really listen to one? The way shakuhachi flute players are trained to listen to one note?
The next time you're at a piano or keyboard, listen to a C major chord. 3 notes; a triad. C, E, and G, played at the same time.
Start by simply taking in the sound. Absorb it. Pretend like you've never heard it before. Hear it with fresh ears. Whatever it takes.
Then try to hear each note individually while still playing the whole chord. Can you hear the C? The E? How about the G? Keep trying. After a while each note will begin to pop out at you.
Each note is special and has a unique function within the chord.
The C is the root. Without the C, it wouldn't be a C chord. It might be an incomplete E minor. So we need the C to define the chord name. (We can sometimes leave it out in the context of a chord progression, but by itself we need the C.) The third, E, defines its quality. Leave out the E and we don't know if it's major or minor. It could be an open fifth like in hard rock or Gregorian Chant for all we know. So the E stays in. G, which is the fifth, is a little more optional. The fifth of a chord adds "body" to the sound, but doesn't influence the effect as much as the other notes. I like to think of a chord's fifth as a "thickening agent," like mashed potatoes can be in soup, or corn starch in Chinese cooking. They don't affect the taste as much as add texture. Fullness. You can leave out the G and its still more of a C major chord than its not.
But for now we have a triad. 3 notes that work together to make a rich tapestry of mingling overtones. We take chords for granted these days, but keep in mind that music was melody only, or melody over a single bass note for most of history. Chords are only a thousand years old, except for isolated periods in ancient history about which we don't know much. Socrates, for example, probably didn't hear many chords.
Spend a little time listening to chords. Become fascinated by them. 3 notes that work together to make something new!
Here's a way to improve your piano playing in whatever style you play. Good luck!