Why does Winston find the prole woman "beautiful?" What is significant about her song? Consider not only her singing of it, but lyrics and the source of the song. What conclusions does Winston come to regarding her and the proles?

As Winston's love for Julia deepens, he regains his humanity. He feels especially human when he can be with Julia in the room above Mr. Charrington's shop.
Shortly before his arrest, Winston gazes out the window at the older woman who is always in the courtyard hanging laundry and singing the same tune. For the first time, he sees her as beautiful:

As he looked at the woman in her characteristic attitude, her thick arms reaching up for the line, her powerful mare-like buttocks protruded, it struck him for the first time that she was beautiful. It had never before occurred to him that the body of a woman of fifty, blown up to monstrous dimensions by childbearing, then hardened, roughened by work till it was coarse in the grain like an over-ripe turnip, could be beautiful.

He finds her beautiful because he is more and more able to see other people as fully human, not just as things. If the Party has taught him that it is perfectly normal to kick the severed hand of a person who has been hurt by a bomb into the gutter, Winston's relationship with Julia teaches him to see the beauty in the world. He also finds the prole woman beautiful because he believes that the hope for humanity lies in the ordinary behavior of people like her. They live in families, have children and grandchildren, care for these children, and lead everyday human lives, just as people have done for thousands of years. Winston believes that eventually, people like this prole will wake and throw off the totalitarian regime.
As for the women's song, the lyrics are below.

It was only an ‘opeless fancy.It passed like an Ipril [April] dye [day],But a look an’ a word an’ the dreams they stirred!They ‘ave stolen my ‘eart awye!

The song is ground out by a machine without any human input, yet the woman's "contralto" voice is so beautiful that she lends humanity and warmth to the soulless song. The song also tells the story of Winston's love for Julia: it is a hopeless dream, it passes quickly like an April day (and may have begun in April, as the bluebells surrounding them the first time they make love bloom in April and early May in England). A "look" and "word" (note) from Julia does stir Winston's dreams, and she does steal his heart away.