What does it mean to be a standard deviation away from the mean?

I think you mean Mean Absolute Deviation or MAD. It means the average amount the digits are from the mean, so let's say the mean is 4 and the digits are 2, 6, 4. So find the difference of each digit 4-2=2 6-4=2 and 4-4=0. So you have 2, 2, 0. Now find the mean of those 3 numbers which will be 4/3.