Prior to his disappearence over the English Channel just before Christmas 1941, Madge had helped out the Doctor in 1938 when he fell from a sub-orbital spaceship into a field she was cycling past. He told her he would return the favour if she made a wish. The Doctor kept his word and returned to give her children the "best Christmas ever".
Her efforts to save her children and herself from the Wooden King and Wooden Queen caused Reg's original disappearance over the channel, but in the same moment, he was returned safe and well due to her strength as both a female and a mother as she set the souls of the Androzani trees free.
Later, as the Doctor bade farewell to her, Madge insisted he spend Christmas day with family. Madge's persistence led to the Doctor visiting his in-laws, Amy Pond and Rory Williams, for Christmas dinner in 2013. (TV: The Doctor, the Widow and the Wardrobe)
Madge had a habit of taking in "waifs and strays" and could even come across as slightly dotty. When her family was threatened, she revealed a steely determination, pulling a gun on the harvest rangers, taking control of their futuristic tripod, braving acid rain and piloting through the time-space vortex with a forest in her head. She was also kind enough to help strangers in need. (TV: The Doctor, the Widow and the Wardrobe)