Q# code is run on a quantum virtual machine; which is a program that simulates a quantum computer on a classical computer.
Quantum computers can be simulated by classical computers up to a certain point. Like that article says, a 30 qubit quantum computer can be simulated on a laptop. Microsoft is simulating up to 40 qubits on Azure. Simulating around 50 qubits or so would need one of the world's most powerful supercomputer.