Since most people don't understand the difference and the MSM doesn't bother to explain I located a diagram of levee construction
around New Orleans. If they aren't high enough water might go over the top, but they don't normally breech.
This is a picture
of the structure that failed, a floodwall.
The pumping system in New Orleans could have handled the levees being overtopped, as it has in the past, but it had no chance when floodwalls broke.
The decision was made to construct canals between Lake Pontchartrain and the Mississippi years ago and rather than using levees a decision was made to use floodwalls, which are inherently weaker structures even when properly constructed.
The quick and dirty solution would be to block the canals while new structures are being built, and before the next hurricane strikes, but that would affect shipping interests and businesses along the canals that have come back.
As it stands now, the people who return can only hope New Orleans doesn't get hit again and store nothing of value on the first floor.