Why did Madge give Katniss the mockingjay pin?

Question

When Katniss volunteered in the 74th hunger games, her friend Madge, the mayor's daughter visited her and gave her a mockingjay pin and was very insistent that Katniss should wear it in the games:

Madge walks straight to me. She is not weepy or evasive, instead there’s an urgency about her tone that surprises me. “They let you wear one thing from your district in the arena. One thing to remind you of home. Will you wear this?” She holds out the circular gold pin that was on her dress earlier. I hadn’t paid much attention to it before, but now I see it’s a small bird in flight. “Your pin?” I say. Wearing a token from my district is about the last thing on my mind. “Here, I’ll put it on your dress, all right?” Madge doesn’t wait for an answer, she just leans in and fixes the bird to my dress. “Promise you’ll wear it into the arena, Katniss?” she asks. “Promise?” ~_{The Hunger Games, ch 3}

Why was it so important to Madge? Did she know that mockingjays were the reminder of the Capitol's fiasco to spy on the resistance and thus a symbol of hope? After all, they were the result of the failed jabberjay experiment:

They’re funny birds and something of a slap in the face to the Capitol. During the rebellion, the Capitol bred a series of genetically altered animals as weapons. One was a special bird called a jabberjay that had the ability to memorize and repeat whole human conversations. They were homing birds, exclusively male, that were released into regions where the Capitol’s enemies were known to be hiding. After the birds gathered words, they’d fly back to centers to be recorded. It took people awhile to realize what was going on in the districts, how private conversations were being transmitted. Then, of course, the rebels fed the Capitol endless lies, and the joke was on it. So the centers were shut down and the birds were abandoned to die off in the wild. Only they didn’t die off. Instead, the jabberjays mated with female mockingbirds creating a whole new species. ~Ibid

Why was it so important that Katniss should wear it? Did Madge think that people would recognize the symbol (as Cinna and Rue did) and assist her friend?

Answer 1

It came from her aunt who died in the Hunger Games.

The significance of the mockingjay pin is expanded upon much more in the second book. First, as Katniss and Madge become closer friends, we learn that the pin came from Madge's aunt:

My fingers touched the mockingjay. "Even my pin now. Mockingjays are all the rage in the Capitol, thanks to you. Are you sure you don't want it back?" I asked.

"Don't be silly, it was a gift," said Madge. She tied back her hair in a festive gold ribbon.

"Where did you get it, anyway?" I asked.

"It was my aunt's," she said. "But I think it's been in the family a long time."

Later on, when Katniss and Peeta are watching footage of the second Quarter Quell - Haymitch's Games - they learn that this aunt was a tribute in the Games:

As Maysilee Donner bravely disengages herself and heads for the stage, I catch a glimpse of my mother at my age, and no one has exaggerated her beauty. Holding her hand and weeping is another girl who looks just like Maysilee. But a lot like someone else I know, too.

"Madge," I say.

"That's her mother. She and Maysilee were twins or something," Peeta says. "My dad mentioned it once."

I think of Madge's mother. Mayor Undersee's wife. Who spends half her life in bed immobilized with terrible pain, shutting out the world. I think of how I never realized that she and my mother shared this connection. Of Madge showing up in that snowstorm to bring the painkiller for Gale. Of my mockingjay pin and how it means something completely different now that I know that its former owner was Madge's aunt, Maysilee Donner, a tribute who was murdered in the arena.

_{(emphasis mine)}

Earlier on, and again in this passage, we also heard about Maysilee as being a friend to Katniss's mother:

That was the year Haymitch won...

"I had a friend who went that year," says my mother quietly. "Maysilee Donner. Her parents owned the sweetshop. They gave me her songbird after. A canary."

[...]

"Ladies first!" She calls out the name of a girl who's from the Seam, you can tell by the look of her, and then I hear the name "Maysilee Donner."

"Oh!" I say. "She was my mother's friend." The camera finds her in the crowd, clinging to two other girls. All blond. All definitely merchants' kids.

"I think that's your mother hugging her," says Peeta quietly. And he's right.

Maysilee Donner was twin sister to Madge's mother, friend to Katniss's mother, ally to Haymitch in the Games. It all comes together: the connection between the Games, Katniss and her family, Madge, and the mockingjay pin. It wasn't a symbol of rebellion at that time - it became one only because of its connection to Katniss in her first Games - but perhaps it's fitting that it should have done so.