What is the intuition of using Hadamard gate in quantum fourier transform?

The intuition, roughly speaking, is that the only way that you're going to get some difference between classical and quantum computing is if you are able to prepare qubits in a superposition. If you remain in a basis state the whole time, you just have a classical computation. So, you need superposition. Hadamard is the gate that prepares superpositions at the start of an algorithm, and it's the gate that, either by itself, or with the help of some phase gates in the Fourier transform, converts a superposition back into a basis state so that we can read it out at the end.