Simple physics explanation:
Simply explained, the magnet, when entered in the spiralled copper, will induce a small current in the wire (since it conducts easily electricity), which will then create a magnetic field that will push the magnets and the battery forward.
As the "train" moves further, the induced current in the wires (thus the magnetic field) follows the magnets and battery, causing the magnetic field to follow also and continue to push the "train" forward.
Original DYI directions:
It's possible to get such power using a dry battery, neodymium magnets (super strong magnets which plated with metal) and a bare copper wire.
A point is that a magnet's diameter is bigger than a dry cell battery's diameter.
And an electric current flows to a coil through a neodymium magnets, and a coil will be an electromagnet only in an area between the magnet and the magnet.
The electromagnet and a neodymium magnet poles repel each other at one side.
The other side poles pull against each other.
They work same direction, and it become a big force.
The phenomenon also continues at a movement destination.
Another important point is magnets direction:
(e.g.) North/South-Battery-South/North.
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