The movement of charge creates a magnetic field. Current (like in a wire) is just moving charge.
The magnetic field forms loops around the wire. By making a coil, every loop of wire adds its magnetic field together inside the coil.
Every loop you add is another set of magnetic fields being added to the coil.
Any other stack of the same shapes will produce the same effect as long as you don’t change the direction the current goes around, but a circle has the benefit of the magnetic field will be uniform everywhere inside the coil.
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