The coils generate a fast, time-varying magnetic fields that induce a time varying electric current inside the metal ball. While doing so, the induced currents in the ball exhibit a magnetic field that is opposite to the magnetic fields generated by the coil. This causes a repulsive force around the ball which counters the earth's gravity. (see for details https://en.wikipedia.org/wiki/Lenz%27s_law )
A side effect of the induced currents inside the metal ball is that these currents heat the ball up to its boiling point and that's why the ball glows red hot. And this is the actual reason for the whole effort, as the levitated molten droplet is used the solder parts that are placed below the coil.