The article has an example: in the unoptimized IR generated by the frontend, all the variables are stored in memory on the stack and accessed through pointers stored in registers, whereas after the mem2reg pass variables are stored directly in registers.
Memory is mutable whereas SSA registers are immutable, so the compiler frontend just put all the C variables in memory to express the semantics of the C program in the simplest way possible. The mem2reg pass then moved all the variables into SSA registers, by simply creating a new register for each assignment and adding phi nodes to track the flow of variables between basic blocks (like the individual iterations of the loop body).
You should read that only after you understand SSA and Phi functions in particular. Once you know how Phi works, the next question is the algorithm for how they're constructed.
