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Fine music is in Agatha's blood. Her ancestors were all classically trained musicians, and although those days are long gone, she spent her 76 years perfecting the violin until she matched their caliber. She is a kind old woman who feels she is too old to fear the wasteland. Fate must smile upon her, because she's still alive. She speaks gently and carefully chooses her words, having been well educated. She spends many a lonely night looking out across the dunes and waiting for someone to come along and help her retrieve the Soil Stradivarius; a lost violin that her great-great-grandmother once possessed.
When she was younger, she married a man called Egglebrecht. Later on, they moved to their shack, and locked themselves away from the rest of the world. A caravan came by every so often, and Agatha paid them in music. Mr. Egglebrecht died a few years ago.
Agatha's Song: Agatha tasks the Lone Wanderer with a two part quest called Agatha's Song. If you give mean responses to Agatha, you will not be able to begin "Agatha's Song" no matter how much time passes.
If you kill Agatha after completing the Agatha's Song quest, her music and voice can still be heard on Agatha's Station, because, as said in dialogue, her broadcasts are pre-recorded.
If you have a high enough Charisma, the Lady Killer perk, or can pass one of the two Speech Challenges, she will give you the key to her ammo box.