My understanding is that the "magic" of a quantum computer is that it quickly finds a solution in a search space that grows exponentially based on the size of the input. Therefore it can be simulated by enumerating the search space and iterating over it.

The simulation is based on describing the problem in terms of quantum computing and translating that description into a program executable by a Turing machine. The simulation allows testing the utility/correctness of programs for quantum computers.