There are no special prerequisites for this course.
Mathematical logic is one of the fundamental topics in discrete mathematics. In fact, it's used in building the foundation of all mathematics, in general.
It is the science of reasoning, intuition; all done symbolically. Having its roots back in the time of the ancient Greeks, mathematical logic has evolved enormously over the years.
What we know today is a very sophisticated, formal system to work with reasoning.
Understanding mathematical logic is of immense importance if you ought to understand mathematical proofs — how to use given knowledge to derive new things; how to switch between conditionals and their contrapositives to simplify proof work; and so on.