Marian Halcombe is Laura's half-sister on her mother's side. Her mother gave birth to Marian from Mr. Halcombe, who gave her his family name, and when he died she remarried Mr. Fairlie, who fathered Laura. Both girls are orphaned, their respective fathers and their shared mother having died, and so they share a deep personal connection with each other.
"...I am as inaccurate as women usually are, in calling Mr. Fairlie my uncle, and Miss Fairlie my sister. My mother was twice married: the first time to Mr. Halcombe, my father; the second time to Mr. Fairlie, my half-sister's father."
(Collins, The Woman in White, gutenberg.org)
There is a second "Mr. Fairlie," but he is the first's younger brother, and so is uncle to Laura and not related to Marian. Marian and Laura's mother is never named; she is referred to only as "Mrs. Fairlie," after her second husband, and her character is revealed mostly through her letters and Marian's memories. Those letters are crucial in the narrator's understand of the story and the long-running conspiracy created by the family ancestors.