What is a ten year storm?
The term's explanation can be found in National Weather Service Technical Paper 40, found here. You'll need the DjVu Browser Plug-in to view the paper. Realize I'm no expert in this stuff, so you may want to read the entire paper for further perspective.
A "ten year" storm refers to the frequency at which a particular amount of rainfall in a given duration (from 30 minutes to 24 hours) is expected to "return," on average. There are also "one year storms," "two year storms," and of course, "hundred year storms."
TP-40 has a long introductory section about how the data was collected and organized, but the meat of the paper is the frequency-duration maps.
You can browse through the various maps in TP-40 to see for yourself what the various storms are supposed to drop here in New Orleans. For example, the 12/21/06 storm, which dropped about 6 or 7 inches in about 12 hours. This would appear to qualify it as a ten year storm over the 12 hour duration.
For reference, here are the rainfall amounts for various durations at the ten year frequency. Many drainage systems - due to economics - are designed for ten year storms.
Ten year storms in New Orleans:
30 minutes: 2.6 to 2.8 inches
1 hour: 3.2 to 3.6 inches
2 hour: 4 to 4.5 inches
3 hour: 4.5 to 5 inches
6 hour: 6 to 6.5 inches
12 hour: 7 to 8 inches
24 hour: approx 9 inches
If we receive rainfall over any of these amounts in each of these duration periods, then we're into a storm bigger than the typical drainage system can handle. Of course, there are local variations in drainage capacities; the typical quote from local officials is that their system can handle an inch in the first hour and half an inch each hour after that. Like I said, I'm no expert, so I don't know how to explain the discrepancy.
But I can speculate. I bet the inch an hour comes from the 6 hour duration and the 1/2 inch an hour comes from the 12 hour duration. If one were to design for the "instantaneous" ten-year shot of rain (3.2 to 3.6 inches in a single hour), the system would probably be so big as to be unaffordable, and possibly wouldn't work very well for smaller storms.