If “the big short” can explain it then the DOJ can.
There are several good analogies in both the book and the movie (ie. the chef and the fish) that greatly helped me understand the mechanics of it.
What the book and movie don't do (unless I'm forgetting something) is explain how anything involved with the 2008 crisis was illegal - the sole exception being that CDSs are very arguably insurance contracts and should be regulated by insurance laws.