The origins of the Maximoff twins have been a hot topic since they were announced to join the Avengers in Age of Ultron. Especially since there are no Mutants in the MCU do to their rights being owned by Fox.
Fans have speculated that the twins would be Inhumans, as it would account for their powers and lead up to the Inhumans movie. However, a more simple, and frankly more logical, explanation has arisen.
A prequel comic for the movie, Age of Ultron Prelude – This Scepter’d Isle, reveals that their powers came from Loki’s scepter (which is believed to have the Mind Gem Infinity Stone) which was used by Baron Von Strucker (head of Hydra) to unlock powers within them.
This explains a lot of what was said in the post-credits scene in Winter Soldier, as Von Strucker no doubt experimented on numerous people before finding success with the twins.