A crystal is a material with a clear, uniform structure.
A psychic deals with the essence of things. Most of the time, the essence we are looking for is buried deeply, hidden from our sights. Crystalline structure is important for psychics because with crystals the essence is clearly visible - the whole form and structure of the crystal is the essence of it.
A crystal for a psychic is a something like a tuning fork for a piano tuner. A tuning fork gives a clear, distinct sound by which we can align the clarity of our hearing. Similarly, a crystal gives of a clear, distinct psychic vibration and energy by which we can align our understanding and experience of the flow of the psychic world around us.
If you let your psychic energy flow through a crystal, you can achieve different effects. Just by touch and feel (or mental imagination) you can observe the vibrational effect of specific kinds of psychic energies.
It can even be beneficial to apply some attributes of crystalline structure (especially the deep, essential clarity) to our own minds, hearts, and physical bodies.