The correct option to fill in the blank is:

C. need an operation

So the complete sentence would be: "It is essential that he need an operation. His illness seems worse."

However, please note that a more grammatically correct option might actually be "needs an operation," but that option is not provided here. In formal English, "it is essential that he needs an operation" is also acceptable due to the subjunctive mood. Nevertheless, based on the choices given, "need an operation" fits in context.