Danny was Karima's husband at some point before the events of Borderlands 2. Little is known about him.
After Claptrap accidentally destroys the Overlook arena where the Vault Hunter trials are being held, Karima sends the Vault Hunters to give a collection of first aid equipment to Danny, who is waiting at the Holy Spirits church. Claptrap accidentally starts a fire and the church begins to burn. It's implied that the fire might have killed Danny (along with the remaining Vault Hunter candidates, and more of the townspeople), though that is unconfirmed, and at odds with Karima's story in Borderlands 2 that her husband had been thrown into the town Grinder by Handsome Jack.