OMG I love this question. Rasputin is my idol.
Anyway, the reason is that the Czar (Russia's king) had a son, who suffered from a rare disease called hemophilia, in which a person can't stop bleeding even from a little cut. The royal family needed someone to heal their son, so they turned to this rural monk from Siberia called Rasputin, who mysteriously stopped his bleeding. To this day no one knows how he did it, but the parents were so grateful, and they were convinced of his psychic and healing powers, that they gave him more and more influence.
So the short answer is "he healed their son of hemophilia."
You should also read about his death. His enemies, who were mad at his influence, had to poison, shoot and beat him and he didn't die. They finally threw him in a frozen river.
