that 68% is correct in the normal setting
but st deviations do tell you how spread out your data/random variable is.
I have been set a question on why the standard error of the means is significant.
I have come to an answer of because you can tell that 68% of the sample means lie between the population mean and 1 standard deviation either side....etc.
I'm not sure what else to add.
Any help would be wonderful