The question isn't so much "what is Sheridan girls" as it is "who are the Sheridan girls." They are first of all, the sisters with whom Leila is going to the ball. They are secondly, the sisters of their brother Laurie (usually short for Laurence). Thirdly, they all are Leila's cousins: "This is my little country cousin Leila. Be nice to her."
The Sheridans and their cousin Leila are on their way to a ball, the first ever for Leila. She had been raised in the country without benefit of society since their "nearest neighbour was fifteen miles," but now we are to infer that she and her mother have moved to the city as she begs her mother "to ring up her cousins and say she couldn't go [to the ball] after all." The Sheridan girls' names are Meg, Jose, and Laura.
But every single thing was so new and exciting [to Leila] ... Meg's tuberoses, Jose's long loop of amber, Laura's little dark head, pushing above her white fur like a flower through snow.