The phenomenon involved is electromagnetic induction (EMI). For the deflection amount depends upon the speed of movement of the magnet or rate of change of flux. Direction depends on the sense ( towards or away) of the movement of the magnet
Direction of deflection is according to Lenz's law.
The law describing the phenomenon is:
The magnitude of the induced emf in a circuit is equal to the rate of change of the magnetic flux through the circuit.
$$\varepsilon =-\dfrac{d\varphi_B}{dt}$$