Please explain for me what you think James meant when he wrote the following in "The Art of Fiction": "A novel is a living thing, all one and continuous, like any other organism, and in proportion as it lives will it be found, that in each of the parts there is something of each of the other parts" (919).

What James means here is that all sections of the novel are intimately connected. When we attempt to isolate its different aspects for the purpose of analysis, we fail to appreciate it as a unified literary entity.
James maintains that the novel is "all one and continuous," a "living thing." In other words, the novel is like a living being composed of interrelated parts. For example, the head is connected to the shoulders, and the arms are connected to the trunk of the body. No part of the body is separate from the others.
James decries the practice of treating the novel as the sum of categorical, dissected parts. He feels that such a narrow outlook is an injustice to fiction. James argues that we should not discuss literary devices, characterizations, themes, descriptive passages, and dialogue without acknowledging that each affects the other. He maintains that "in each of the parts there is something of each of the other parts."
He laments that we separate the "novel of character" from the "novel of incident," as if the two are distinct entities. James argues that the only distinction that makes any sense is the one between good movies and bad movies (or good novels and bad novels). Everything else is immaterial. After all, "incident" illustrates "character" just as much as "character" determines the outcome of an incident. James argues that the separation of "incident" from "character" is a childish distinction.