Understanding the definition of the standard deviation is much less important than knowing its properties and having a feel for what its numerical value tells you about the data.

Guessing s from histogram

About 95% of the values should be within 2s of the mean, so after dropping the top 2.5% and bottom 2.5% of the values (histogram area), the remainder should span approximately 4s. Dividing this range by 4 should approximate the standard deviation.

Sketching a histogram from the mean and s

Similarly, you should be able to draw a rough sketch of a symmetric histogram with any mean and standard deviation that you are given. (It would be centred on the mean and 95% of the area would be within 2s of this.)