Here's the story: "Believe it or not, since sending Mozart's [music] soaring through their stalls at milking time, Sieber has seen a dramatic shift in the temperament and production of his Daisys and Besses. Now his herd quietly lines up to be milked, seeming not to mind the poking and prodding that comes with being a dairy cow, and, most notably, producing anywhere from 1 to 6 more liters [quarts] of milk per day than their non-Mozart listening counterparts. ... Not only do these now blissful bovines produce more milk, but, as it turns out, their milk has higher levels of healthy fats and proteins and, according to the farm, a sweeter taste. Now, that's music to everyone's ears."
Perhaps listening to Mozart contributes to higher levels of oxytocin and prolactin production by calming a woman (or in this case, a heifer), thus leading to more milk. We know that classical music releases dopamine (the "feel good" reward hormone) in the brain, so it would make sense that it could affect the breastfeeding hormones as well.
Here's the exact piece of music that the dairy farmer plays, in case you want to give it a listen next time you sit down to breastfeed.