Why is $\mu$ finite looping?
It is said that the intuitive meaning of μ is finite looping where as the intuitive meaning of ν is infinite looping in μ calculus


Here's a better phrasing: µ is about looping with a known bound on the number of iteration. For ν we do not necessarily know the bound, and there may in fact not even be one.


  Is there any theorem which proves this ?


Theorems can not prove how apt an intuition is. The property you have in mind follows from the definitions and can be illustrated by some examples.