Story points are a relative unit of measure to assess whether a user story is big or small (so how complex it is). It basically tells you and the rest of the Agile Team whether the user story is low, mid or high complexity compared to other user stories.
You can use different scales for story points (e.g. a very simple one such as 1 (low complexity user story), 3 (medium complexity user story) and 5 (high complexity user story); t-shirt sizes s, m, l, xl, xxl, a more complex scale such as the fibonachi sequence or even your own made up scale.
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