what does it mean by problem of size $0$? I am having problems understanding a basic concept in CLRS, it is about worst case partitioning during quicksort -- 


  The worst-case behavior for quicksort occurs when the partitioning routine produces one subproblem with $n − 1$ elements and one with $0$ elements.


What does it mean by subproblem of size $0$? But what I see is there will be two subproblems, one with size $n-1$ and another with size $1$. I fail to grasp the idea of $0$ size. 

Can someone explain?
We're talking about algorithms to sort a list.  Therefore, in this context, a problem of size 0 is a list of size 0, i.e., the empty list.

Quicksort splits a list of size $n$ into two sublists of size $m$ and $n-m-1$.  They sum to $n-1$ (not $n$), because quicksort removes the pivot element: the pivot element is not included in either sublist.  Therefore, the text you have quoted is correct.  If one sublist has size $n-1$, then the other will have size 0 (not size 1).