McPhee wrote a long New Yorker article that's a short version of the book. Contains the basic info you need to understand the drama.
Here's a great Google Maps view of the spillway. Try looking at it in street view! Fascinating.
Here's the scoop. Every thousand years or so the Mississippi River changes course radically, and starts building a new piece of the delta. Physics causes this. The water is always seeking the shortest and fastest route to sea level, the Gulf of Mexico. Over time the river deposits silt that it has to flow over, causing the route to be longer and slower. Eventually in a spring flood it rises over one of its upstream banks and digs a new channel and flows in a different direction.
Well, the most recent milennium was over around 1950 or so. Since then the US Army Corps of Engineers has been at war with the river, trying to keep it flowing past Baton Rouge and New Orleans, and all the industry that's built up around the cities. And away from places where people live now, that would be underwater if the river changed course.
This year's flood may be the moment. If the river tops the levees in the place the river is trying to shift direction, it's going to be super-hard if not impossible to get it back into its current banks.