The nail sticks to the magnet due to the magnetism in the magnet. The magnet induces magnetic domains into the object attached to it such that it magnetic domains in the object are aligned to the magnetic field of the magnet.
The nail will stick to the magnet because it will become magnetized.Also because the north pole in the magnet rearranges the magnet domains inside the steel so that their south poles all point toward the north pole of the permanent magnet
