how does an electrical motor work?

My pestal fan is not working. So I decided to junk it and meanwhile
also take it apart to investigate. I am puzzled by the electrical
wirings so I am asking this question. The elecetrical motor has
bushings on 2 sides with 2 wires black and white. This part I
understand that the wires brings in electricity and rotate the middle
magnet to spin around the outside megnetic coil which is energized by
2 wires +/- AC. The Power cord comes with a white wire that go into
the housing, another lead go into a samll box. This box is outside of
the cyclindrical housing, it is a small 3cmx3cmx1cm box with 3 small
wires black, red, purple ,(box which I can adjust speed). Then another
box 1cmx1cmx1cm with 2 wires blue and grey that look like a resistor.
So there are total 5 wires that go into the motor housing: black,red,
purple, white, gray, blue. I think it only need 2 wires to make a
motor spin. What do the other wires do? If I use a voltmeter to test
each wire, what should I get if it is normal?

.

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