why is Mu-metal in transformers?
Magnetic shielding works by "conducting" magnetic lines of force around the thing to be shielded.



Mu-metal has an unusually high magnetic permeability, which makes the lines of force tend to want to stay within the material.

If you want to keep magnetic fields either in a small space, or out of a small space, you can shield it by building a box of mu-metal around the space.



Afterthought:

The drawing* is not entirely honest: It should show a few flux lines going through the shielded space, but the density of flux lines within the shielded space is less than the density outside.  How much less depends on the thickness of the shield material.



*It's not my drawing; I stole it.