I find the SD useful as a measure of how closely I have managed my blood sugar and in particular, how much I have kept my after meal (and exercise) numbers well controlled. I think for many of us, the SD is not critical. But when you start to push for "tight" control it matters a great deal. The most accurate estimates of SD come from a CGMS, but you can get reasonable estimates from just testing (which is what I do).
At least in my case, my SD helps me predict how "safe" I am. It tells me how likely I am to avoid lows. 95% of my readings will be within two standard deviations of my blood sugar average. If I want to lower my average blood sugar (and hence my A1c), I need to tight up my SD or I will have lows.
If your A1c is say 7%, then a good way of estimating your target SD is to figure that an A1c of 7% corresponds to an average blood sugar of 154 mg/dl. If you want to have 95% confidence that your blood sugar readings won't go below 60 mg/dl, then you want your SD to be (154-60)/2 = 47. If you tighten things up and want an A1c of 5.5% and don't want to go below 60 mg/dl, then you need an SD of 25.
ps. And I apologize for the math