I'm sure all sorts of things can cause a piece of music to affect us emotionally. Sometimes the lyrics can have the effect. Sometimes a song will remind us of a situation or person from the past, that triggers emotions. Sometimes the music or singing is itself so utterly beautiful to our ears that we are moved by it. I sure a mixture of any or all of these frequently happen too.
Oh, I find that alcohol makes a big difference too !
Almost the whole of Philadelphia by Bruce Springsteen has an effect on me. Quite strange, as I don't like anything else he's ever done really.
Also, I find the guitar solo in "the Grapes of Wrath" by Spear of Destiny to be utterly moving, just by it's shear beauty. It's such a dark, desperate, and tragic song, and the solo fits it so perfectly.