Some of these pictures and descriptions may give away plot details that you might not want to know before watching the film.
This is a ghost story based on the Henry James novel "The Turn of the Screw" that is set in a mansion in England during the Victorian era. It appears that the spirits of the former governess, Miss Jessel, and a valet she was involved with, Peter Quint, have possessed two children. This can also be interpreted as happening only in the mind of a mentally unstable governess, or that the ghosts represent the children's repressed memories of terrible things they experienced involving the now-dead servants. In the movie (but not in the book as far as I can determine without re-reading it) the girl Flora has a pet tortoise. A tortoise, which hides in a thick shell to avoid danger, can be interpreted as a symbol for this repression. But enough of that. This isn't English 1A, just an illustration of herps in movies.
When Miss Giddens, the children's new governess played by Deborah Kerr, first arrives at the estate and meets the young girl Flora, Flora asks her if she is afraid of reptiles because she wants to show her the pet tortoise named Rupert she keeps in a pocket of her dress. Later Flora asks Miss Giddens if tortoises can swim, then takes Rupert out of the water at the edge of a lake and dries him off. Finally, during a climactic conversation in the greenhouse between Miss Giddens and Flora's brother Miles, he becomes so angry that he takes the tortoise, which he has been holding in his hand, and throws it through a window pane - the same pane on which we saw the ghostly face of Peter Quint just before it broke. He throws the tortoise, a symbol of repression, and smashes the "ghost" responsible for his repression, after which the boy yells Quint's name to Miss Giddens. Looks like we're back to English 1A. Class dismissed.
A live tortoise (or probably more than one) is used in the movie, but I don't know what species.