Notes played together can sound dissonant or consonant or anywhere in between. Dissonant(non-harmonic) notes sounds like they are fighting each other and consonant(harmonic) notes sound like they belong together. Adding non-harmonic (dissonant) notes can add color, shades and interest to the music. It makes the music much more expressive.
One time when Mozart was very little his father heard him playing many different combinations of notes together. Father asked Mozart "What are you doing son?" Mozart said "I'm finding music friends!" In other words consonant notes! When you listen to his music, it is much more consonant than most - especially some 20th century classical composers.