Question: I am a PhD student in Mathematics. I wanted to know what exactly is the difference between PhD and Postdoc. Is it just the research that one does after PhD(kind of second PhD?)?

Answer: 
In mathematics, a "postdoc" is a special kind of faculty job you get just after your Ph.D. It may have a fixed term (not tenure track). It may have reduced teaching, so that you can concentrate on your research. You may have a "mentor" assigned to advise you on doing research.

But (unlike some other fields like experimental physics) you are probably not working in someone else's "lab" on someone else's research program that someone else got the funding for.
This is akin to asking what's the difference between research master's and PhD, or Assistant to associate professor.

A postdoc, is the *next level* after PhD (though not a necessary one). This is the main point.

Practically, it is different, in that it is less formal, with less specific requirements, and you are paid for it, as you are employed, not a student, as other answers here explained well.