induced e.m.f for a coil of wire depends on four things:
Magnetic strength of the core in the coil of wire. (stronger --> bigger emf)
Number of turns of wire in the coil (more turns --> bigger emf)
The cross-sectional area of the coil (bigger area --> bigger emf). (This could also be seen as the angle you point the magnet at the coil, because flux linkage is basically the same as flux cutting.)
How fast you move the magnet into/out of the coil. (Faster --> bigger emf)