Definition of Perfect Elimination Ordering?

The answer to this question could be trivial !

Definition:

A perfect elimination ordering in a graph is an ordering of the vertices of the graph such that, for each vertex $v$, $v$ and the neighbors of $v$ that occur after $v$ in the order form a clique.

I'm not sure if I understand completely the definition .

Question?

Could somebody explain a little bit the definition, or give some example to illustrate the idea ? ( I have not understand the following sentence "that occur after $v$ in the order")

Any idea will be useful!

2. For each vertex ($v_i$), take the set (S) consisting of {$v_i$} $\cup N_j(v)$ where $Nj$ is the neighbours of v with position in the ordering > i