When describing the reduction of an undecidable language to another, we use a partial function. I understand that the left side of the function is the undecidable language such as the halting problem, but what does the format of the right side mean. I understand it's our new problem, that we want to show is undecidable, but whats the general format of such arguments and what does it mean?

i.e. f(M,w) = ??? where M is the Turing machine that decides if M halts on input w.