It's the (expectation) value of a loop of variables, each of which takes one of the values 1 or -1 along adjacent parts of the loop.  However the reason it's useful to compute it at all is in the dynamics of these variables and how these are coupled to the rest of the system. It doesn't make sense otherwise.

Dear Chiranjit Mondal

Read the following site may be help you

"http://physics.stackexchange.com/questions/167655/compute-z-2-invariant-of-2d-topological-insulators-without-computing-the-eigen"

Dear Mondal,

There are various techniques to find out the Z2 invariant of TIs but most of them have complex calculations. There is a this topic which seems a bit easier just go through it once and the other link has a python code recently developed to calculate the same. Please find whichever is convenient for you.

http://www.worldscientific.com/doi/abs/10.1142/S2010324711000057

http://z2pack.ethz.ch/doc/

Dear Anvesh

Thanks for your suggestion.  The system for which I am intended to calculate Z2 index is inversion symmetric. So simply computing parity at the TRIM we can calculate Z2 index as suggested by prof. Ken & Male. Do you know how to calculate parity of a band at any high symmetry point? Please let me know.

I tried to run the python package ( Z2pack) that you suggested above but I am facing some problem to run that.  

thanks