Scientific experiments often require comparing two (or more) sets of data.
For example, paired data can arise from measuring a single set of individuals at different points in time.
[1] A clinical trial might record the blood pressure in a set of n patients before and after administering a medicine.
In contrast, another clinical trial might measure n patients before treatment and a different set of m patients after treatment; in that case, the "before" and "after" data are unpaired.
Statistical tests used to compare sets of data have been designed for data sets that are either paired or unpaired, making it important to use the correct test to prevent erroneous results.