Final answer:
The best description for an undecidable problem is that it lacks a general algorithm for determining solutions, illustrating the complexity in computability theory and dealing with Turing machines.
Step-by-step explanation:
The statement that best describes the characteristics of an undecidable problem is (C) An undecidable problem lacks a general algorithm to determine its solutions. In the context of computational theory, an undecidable problem is one for which no algorithm can be constructed that will always lead to a correct yes-or-no answer. This means that there's no procedure with finite steps that can be applied to every instance of the problem to determine a solution.
Problems such as these arise in the study of computability theory and Turing machines, where certain decision problems cannot be solved by these abstract machines. An example of an undecidable problem is the Halting Problem, which asks whether a given computer program will finish running or continue to run forever. No general algorithm exists that can solve this problem for all possible program-input pairs.