If you place the wire near a permanent magnet, this temporary magnetic field interacts with the permanent magnet field. You will know that two magnets placed near one another either attract or repel. In the same way, the temporary magnetism around the wire attracts or repels the permanent magnetism from the magnet, and that is what causes the wire to jump.
Think of the atoms of magnetic material as an unruly herd of cattle. Running electric current through the material will polarize these atoms, creating the magnetic field. But as I mentioned, this is an unruly herd, so it takes time for the current to bring all those atoms into formation.