Wanda Maximoff aka Scarlet Witch was one half of the superhuman twins abducted by the High Evolutionary. As the story goes, they were abducted when they were babies, experimented on to achieve undesired results, and then returned to their parents Django and Marya Maximoff in Wundagore. As for all mutants, their abilities were realized and manifested when they reached puberty. In the unfortunate incident of Django being attacked by villagers because of stealing food to feed his family, Wanda's twin brother Pietro aka Quicksliver uses his hyper speed to help them escape. For a few years they lived around Europe as nomads, under the radar.
Even as a young adult, Wanda was not able to control her powers. As a result ,she accidentally causes a house to burst into flames, and the townspeople reacted in violence thinking that she was a witch. Although Pietro tried to help them both escape, they were overpowered and just as they were about to be sentenced, they are rescued by Magneto, who also convinces them to join his team - the Brotherhood of Evil Mutants. It is with the brotherhood that they were given their aliases Scarlet Witch and Quicksilver. They fought with the brotherhood for a few months, even against the X-Men for a while until Magneto finally met his match - an alien being called Stranger. Stranger defeats Magneto and transports him to outer space. It was then that the twins decide to quite the brotherhood.
Later on, the twins discover the Avengers and go on to seek help from them. They are recruited into the squad and molded into and trained to become better people and superheroes.
In the Marvel Cinematic Universe (MCU) storyline, Wanda and Pietro join the Avengers upon learning about Ultron's maniacal plan to destroy humanity. In the battle against Ultron, Pietro sacrifices himself to save Hawkeye. Following the death of her brother, Wanda is officially recruited as a new member of the Avengers together with Vision and Falcon, and they fought every battle with the Avengers henceforth. Wanda took a liking to Vision and the two eventually fall in love.
After the Sokovia Accords, Wanda and Vision decide to lead their own private life away from trouble, but as heroes, trouble always finds them. They are attacked by Thanos' henchmen in an attempt to retrieve the Mind Stone from Vision. The first fight was won as soon as Captain America and Black Widow showed up to aid them. Learning Thanos' intention to use the Mind Stone as part of his Infinity Gauntlet to wipe out half the universe, they seek help from Suri, Wakanda's best scientist to remove the Mind Stone. Sadly, Wakanda is attacked by Thanos' army and Vision is killed before the procedure could be completed. The Snap happens, and Wanda disappears from existence until after the remaining members of the Avengers manage to reverse its effects.
Driven by vengeance, Wanda rejoins the Avengers with the aid of all other superheroes in the MCU to finally defeat Thanos and his army.
A fun fact about Quicksilver and Scarlet Witch: Although they are believed to be the children of Django and Maya Maximoff, it is later revealed in the comics that they are actually the children of Magneto.