What is the question that Mach tried to address in his principle? I mean, we know how to detect the inertial and non-inertial frames (by Newton’s law). Once this is understood we also see that due to the acceleration of a non-inertial frame pseudo forces appear. Since there is no privileged inertial frame the acceleration of a non-inertial frame is quite unique i.e., one and the same with respect to every inertial frame. Right? So what extra does the Mach’s principle try to answer? I’m a little confused.
EDIT : I have read that Newtonian theory doesn't attempt to answer the question that what is the physical origin of pseudo forces but Mach's principle does (see "Introducing Einstein's Relativity" by Ray D'Inverno). I thought this is due to the acceleration of the frame itself. I think what Mach meant is that local inertial frames are determined by global mass distribution in the universe. And if that mass distribution changes then the local inertial frame changes to a non-inertial one and gives rise to pseudo forces. I don't know but this is the impression I have. I may be totally wrong.
Next I also wanted to ask is it really essential to understand Mach's principle or Newton's bucket experiment to understand general relativity? Is the idea/definition of frames based on Newton's law insufficient to understand frames in general relativity?