The song tells the story of the video. Three people who are just living their lives, which are difficult. The nurse/mom works hard and her child is lonely and runs away so she is stressed out, worried about her child.
The woman is abused by her drunk husband/boyfriend (beauty going out with an idiot) and decides to leave (a change in heart comes slow).
The bum picks up the dog thinking he is going to make some money with an act.
The woman meet by chance and so do the bum and child. The child realizes running away is not a good idea, after seeing the bum and goes home (baby you know I'm not alone).
The rest of the video is "the happy ending" Mom and child are together, the two woman become friends, the dog finds his owner and the bum gets a meal, but nothing is really answered. Everything takes time to change slowly, slowly now.
Anyway that is what I get out of it.