A mystic, Rasputin had strange healing powers. When no one else could help Alexei's bleeding disorder, Rasputin made the bleeding stop. When the family thought Alexei would die, Rasputin helped him get well. Alexandra, obsessed with guilt for passing the dreaded disease to her son, began to depend on Rasputin for everything.
Years later, people realized Rasputin most likely hypnotized the tsarevitch. At the end of the 20th century, doctors know that such a procedure sometimes helps hemophiliacs. But at the beginning of the century, Rasputin's powers seemed almost magical - especially to the Empress.
Because the Imperial Family had kept Alexei's hemophilia a secret, no one knew why Alexandra was so protective of Rasputin. Many people believed Rasputin, a well-known womanizer, was having an affair with the Empress. Despite his slovenly appearance and habits, Rasputin had total access to the royal family. (Follow the link to view rare film footage of them.) This shocked even the aristocracy. Contemporary newspapers contained caricatures depicting Rasputin's hold over Nicholas and Alexandra.
Members of the extended royal family began to believe Rasputin was a de facto member of government. Because Nicholas II often followed the advice of his wife, and because Rasputin was advising Alexandra on affairs of state, the royal family took matters into their own hands. Rasputin had to go.