Why does Helen Stoner come to see Holmes in "The Adventure of the Speckled Band?"

The short answer to this is that Helen Stoner, in the story “The Adventure of the Speckled Band,” comes to see Sherlock Holmes because she fears that someone is going to try to kill her.  The longer answer explains why she believes someone wants to do so.

Stoner lives with her stepfather, who is a doctor named Grimesby Roylott.  He married Stoner’s mother when Helen was a little girl in India.  Helen’s mother had “a considerable sum of money” that she gave to Roylott when they married subject only to the stipulation that

a certain annual sum should be allowed to each of us (Helen and her sister) in the event of our marriage.

Helen’s mother is now dead, having been killed in an accident 8 years before the story is set.  Helen’s sister has also died, in suspicious circumstances at Roylott’s ancestral family home.  She was engaged to be married at the time that she died.  Now, Helen is engaged to be married and fears that she, too, will be killed.

Helen, herself, does not say that she suspects her stepfather.  However, she does talk about how violent he is and she reluctantly shows Holmes marks on her wrist where he has grabbed her.  She fears that she will be killed, though, because Roylott has recently had her move into the room where her sister died.  She has also heard strange sounds that her sister reported hearing soon before her death.  Therefore, she worries that she will die just as her sister did.  She does not specifically say that she suspects that her stepfather will kill her, but it seems clear that she is at least subconsciously aware that he might be a danger to her.  This is why she comes to see Holmes.