Basically, Alessa was a girl who was concieved without knowledge of her father. As she grew up the religious fantatics of Silent Hill regarded her as an incarnate of sin (a witch) for whatever reason and decided to try and burn the sin out of her.
She survived but was horrifically scarred. This torment caused her to release a demon into Silent Hill which is a representation of Alessa's evil side (maybe she really was a witch). It wants revenge on those who wronged Alessa. However it cannot enter the sanctuary that the residents of Silent Hill have built within the church.
Basically the misty, ashy Silent Hill is the reality that Alessa created so that Silent Hill residents would be unable to leave, as eternal punishment. She can bring whomever she wants into this reality. But there is no way out, they are trapped forever (explains the ending).
She can also transform it into a hell version of the purgatory at will, which is when demons are unleashed. There are three realities in Silent Hill. Normal (Sean Bean enters this one) Purgatory (Rose comes here) and Hell (Demon Alessa's is here).
This is a place of nightmare where Alessa can create warped creatures, her version of people who wronged her (Colin, the janitor is the one who raped her, the grey children at the beginning are the school children who teased her, the monster in the straightjacket represent the fanatics who are bound by this religion of hatred).
Sharon was created by Alessa and is full of burned Alessa's good side. She was sent to an orphanage and eventually mothered by Rose. This is how Alessa brings Rose into Silent Hill, to reveal to her through Sharon, the truth about who Alessa is and what happened to her.
By doing this, it will create enough sympathy in Rose to allow demon Alessa to breach the sanctuary of the church through Rose's body (you see demon Alessa go into her, mother is god in the eyes of child and all that) and thus allow burned/evil Alessa to intertwine and have their sadistic revenge.
Since Rose and Sharon have entered Silent Hill's purgatory, they cannot leave, and thus are trapped in that reality. However with Sharon/Alessa with her, she can leave Silent Hill town and go to her home but still in that reality (due to Alessa) and is also why Sean Bean still can't see her.