What does a high/low standard deviation mean in real terms?
The higher the standard deviation the more variability or spread you have in your data.
Standard deviation measures how much your entire data set differs from the mean.
The larger your standard deviation, the more spread or variation in your data. Small standard deviations mean that most of your data is clustered around the mean.
In the following graph, the mean is 84.47, the standard deviation is 6.92 and the distribution looks like this:
Many of the test scores are around the average. There's one student who scored a 96, two students who scored 69, another two who scored 71, but most students scored close to somewhat close to the average of 84.47.
In this second graph, the mean is 80, the standard deviation is 14.57 , and the distribution looks like this:
There is greater variability in the test scores. One student scored a 24, which is pretty far from the average test score of 80. Another student scored a 45, which also isn't close to 80.