Definition off site:
https://statistics.laerd.com/statistical-guides/measures-of-spread-standard-deviation.php
The standard deviation is a measure of the spread of scores within a set of data. Usually, we are interested in the standard deviation of a population. However, as we are often presented with data from a sample only, we can estimate the population standard deviation from a sample standard deviation. These two standard deviations - sample and population standard deviations - are calculated differently. In statistics, we are usually presented with having to calculate sample standard deviations, and so this is what this article will focus on, although the formula for a population standard deviation will also be shown.

http://www.une.edu.au/WebStat/unit_materials/c4_descriptive_statistics/standard_deviation.htm
The standard deviation (for a sample) is defined symbolically as
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Definition in my own words:
its when we calculate the true standard deviation by collecting samples from a population