We covered the pigeon lady in the character section, but she's really more of a symbol than a character. So we're going to rewind: what's this lady's deal again?
Well, she exists as a character in a song Mary sings—and then she exists in real life. She sits outside St. Paul's Cathedral, feeding pigeons, and sells little bags of birdseed so that other people can feed the pigeons too.
Mary describes her in song:
MARY: Feed the birds, that's what she cries, while overhead her birds fill the skies. All around the cathedral the saints and apostles look down as she sells her wares. Although you can't see it, you know they are smiling each time someone shows that he cares. Though her words are simple and few, listen, listen, she's calling to you. Feed the birds, tuppence a bag. Tuppence, tuppence, tuppence a bag. Though her words are simple and few, listen, listen she's calling to you. Feed the birds, tuppence a bag. Tuppence, tuppence, tuppence a bag.
All you need is tuppence—that's just two pennies. Michael has tuppence in pocket, which he wants to use to feed the birds after he sees that the bird lady really exists. When Dawes Sr. tries to make him put that money in a savings account, Michael rightly resists, though it ends up getting his dad fired.
As one of the songwriters of "Feed the Birds," Richard Sherman put it, "The song "Feed the Birds" has nothing to do with ornithology: it's about how it doesn't take much to give love." (Source)
All you need is tuppence, and you can make a bunch of birds—not to mention a certain bird-lady—way happier. It's a lesson that George Banks needs to learn, and which his kids and Mary Poppins can teach him.
We just have one little qualm about this situation: pigeons? Really: pigeons? The rats of the skies? Couldn't the brains behind Mary Poppins have come up with a nicer bird to feed? You know those pigeons are already getting fat off of old French fries.