EDIT: I failed to mention that the system's inverse also needs to be causal and stable. I cannot wrap my mind around on how when a system and its inverse are both causal and stable and LTI IIR it is safe to say that the system is also minimum phase.
So the causality for a system means that $$h[n]=0, \mbox{for all } n<0,$$ but what does the stability mean when talking about a system? That there are no poles inside the unit circle? and if so how does it turn out that when a system is causal and stable it's also min phase.
Also intuition-wise when is a system inverse causal and stable?
I should clarify that I'm talking about discrete time.