David Shariatmadari suggests some answers in The Guardian.

• What’s happening? An “autonomic nervous system arousal, the evolutionarily ancient preparation for fight or flight.” Plus a positive emotional component, related to brain activity and dopamine release.
• To whom? Not to everybody. According to some estimates, only to every second non-musician.
• Why? Emotional experiences can be related to specific musical structures like “enharmonic changes” or “appoggiaturas” (examples given in the article), connected with unexpected, dramatic shifts that force the listener to pay attention. Add to this memories and “feelings of transcendence.” Maybe music helps to form bonds with other human beings or it played a role in the development of language. “Music simply taps into [linguistic ability] in the same way that drugs tap into a system that wasn’t designed for drugs”.
• Example: “The last few minutes of Bach’s Mass in B Minor, the last page or so of the Dona Nobis Pacem.”