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Subha and Nisumbha (nikhumbha) are asuras (demons) did a long penance (tapas) and Brahma was pleased to grant them boons. They asked for power and being undefeated. They asked for a boon in the hands of a virgin woman who is not (born to parents in the normal human way) and who is not married. 

These two brothers are descendants of Hiranyakasipa. They fought Devi Durga seeking revenge after their relative Chanda and Munda were killed by her. They were killed by her. To kill them, all the Gods had given their powers to Devi Durga. 

This story appears in Devi Mathatyam (puran) and appears to be told by Maharshi Markandeya.

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Sumba and Nisumba were two Asuras or demons who confronted and were ultimately defeated be Devi Durga. They had performed a long penance to gain the boon of not being able to be defeated. 
They had confronted the Devi to seek revenge because she had killed their relatives Chanda and Munda. To defeat these demons, all of the gods had blessed Devi.