What the induced emf depends on

As the magnet and coil come closer together or move apart, the number of field lines linking the coil increases or decreases. The galvanometer deflects only then, so for an emf to be induced in the coil, the number of field lines linking it must change.

When the magnet moves quickly the galvanometer deflects more than when it moves slowly. That is because the coil's induced emf is directly proportional to the rate at which the field lines change.

Faraday's experiments showed that some of the factors affecting the size of the induced emf are:

Why each one helps

Each turn of the coil has its own small emf induced in it, and the turns are joined one after another like cells in series, so twice the turns gives twice the emf. A stronger magnet has more field lines, so the same movement changes the number through the coil by more. Moving faster makes the same change happen in less time, which is a greater rate of change. All three increase how fast the field lines through the coil change, and that rate is what the emf follows. Compare this with the motor: there, more turns, a stronger field and more current give a bigger force. The same parts matter both ways round.