What is the significance of Max Q in rocket launches and disasters?

[Devils]

So I was reading about the challenger disaster and came across this report:

http://history.nasa.gov/rogersrep/v1ch3.htm
Both the Shuttle main engines and the solid rockets operated at reduced thrust approaching and passing through the area of maximum dynamic pressure of 720 pounds per square foot.

I listed to rocket launches & they all seem to mention MaxQ but have never seen a value. From the report, 720 pounds per square foot = exactly 5psi. A typical car tyre is 30psi, so the maximum pressure on the space shuttle is about 1/6 of that of a car tyre.

That seems low to me so why mention it at all? The recent SpaceX was near Max Q so was that part of the problem, is was vibration the problem? What is Max Q for an airplane?

 

[Lsos]

I don't know what I'm talking about, but just from a quick glance, a tire is small and the pressure is distributed nice and evenly, over a smooth profile. And if you make the tire 2-5 times stronger than it needs to be, well no big deal. On a space shuttle with an (educated guess) frontal area of 80000 in^2, that 5psi adds up to 400,000 lbs of extra force, squeezing it lengthwise along uneven paths and who knows what, designed to be juuuust strong enough, in a complex machine with a small nuke's worth of explosives. That's definitely something that should be accounted for in the rocket's design.

 

[CWatters]

I don't know what the maxQ of an aircraft is but pretty sure the VNE (Velocity Never Exceed) will be lower for a plane than a rocket perhaps by a factor of five?