What is "Containment order"? Could I get a friendly explanation?
I'll try a down to earth definition \ example:

When speaking of a set $X$, lets say $X=\{1,...,100\}$, 
denote the subset $X_i = \{1,...,i\}$

It holds that $X_1\subseteq X_2\subseteq...\subseteq X_{100}$ 

So you could say there is a containment order over these subsets, because each subset contains the other in an order that I stated. This order came from, and connected to (and isomorphic to) the partial order of $1 \leq 2 \leq ... \leq 100$ or if you prefer more fomally, that $(X,\leq )$ is a poset.