Standard deviation is a measure of dispersion from the center. The standard deviation helps you understand just how spread out the results are among your test-takers. This can help you understand whether most of the numbers are very close to the average or not. 

Standard deviation is calculated by first determining the distance of each score from the mean and then taking the square root.  
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Let's say you have five people take an aptitude test. The maximum possible score on the test is 100. The scores are as follows:
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56, 75, 94, 82, 67
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If you add all these scores together (374) and divide by 5 (the number of tests), you get a mean score of 74.8. From this, you calculate the distance of each from the mean score and then calculate the square root.
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In this example, the standard deviation would be 14.45, which is quite high, meaning that the range of scores was fairly widespread. If, on the other hand, all of your test-takers scored between 90-100, the standard deviation would be much smaller.