Consonance & Dissonance
Consonance and dissonance describe how a combination of notes sits on the ear. Consonant sounds feel settled, resolved, easy to listen to; they reduce tension. Dissonant sounds feel tense, unresolved, sometimes harsh - they create tension. Neither is "good" or "bad": they are the two poles that movement in music swings between.
This matters because real movement needs both. A piece made only of consonance sits still; it never goes anywhere. Dissonance is what makes a phrase want to move, and consonance is the rest it moves toward. The push and pull between them - tension built, tension released - is the engine underneath melody and harmony alike.
Where you hear it
Every interval leans one way or the other: a perfect fifth or a third sounds consonant, a minor second or a tritone sounds dissonant (the Intervals page tags each one). The same is true of chords and of whole progressions, where dominant chords supply the tension that tonic chords resolve. Dissonance is not only made with notes, either - rhythm, syncopation, timbre and dynamics can all create tension too.