The venerable Old Major composed the lyrics to "Beasts of England" in George Orwell's novel, Animal Farm. The song was "a stirring tune," meant to be sung to the music similar to "My Darling Clementine" and "La Cucaracha." Once it was determined that "Beasts of England" was no longer pertinent, Squealer led a group of sheep for a week's practice. When he presented the new song, it was a simple one: "Four legs good, two legs better!" It marked the first appearance of the pigs walking on two legs.
Mollie represents vanity. She is the people of a society who want nothing more than instant gratification and to have their needs met.
Napoleon didn't set things up for Mollie to have her needs met instantly. In fact, he took away everything that she wanted: ribbons in her hair, sugar tablets and most of all, favor of the leader. She had all these things with a human leader and longed to have it again, so she escaped from the farm.
Mollie runs away from the farm because she does not really mind being a work horse for the humans. This may be in part because she pulls Farmer Jones's "trap" rather than a plow or anything like that. All she really cares about is how she looks. She wants to be sure that she will have ribbons for her main and sugar to eat. If she has that, she's good.
Mollie finally runs away for good in Chapter 5. Some days later, some birds see her. She is pulling a cart again -- she has ribbons and seems happy. So -- she has run away so as to get the material things that she wants because she is such a vain, shallow "person."