Coil and Core-What exactly this is?
You need a view from a different angle.



From the Wiki article on galvanometers.

Now you can see that the coil is wound on a lightweight rectangular former, with a bearing in the centre of each end, and this former is suspended between the poles of a U-shaped magnet (broken open in the image to show the coil).

Now there's a huge gap between the magnet's pole pieces which would result in a weak magnetic field, and a very insensitive meter. So the trick is to fill that gap with a fixed iron core, such that there are two very narrow gaps, just wide enough for the former and its coil.

This concentrates the magnetic field in those gaps, and the magnet pole pieces are shaped to linearise it (it should be the same at any angle where the former is in the gap).

The iron core is fixed - if it moved with the coil, its weight would slow down the meter movement. But because it's inside the former, the former cannot make a full revolution, it would hit the core's supports. So this is a great arrangement for a meter, but no good for a rotating motor.