Researchers perform cointegration tests when time series are nonstationary to determine whether they have a stable, long-run relationship.
xtcointtest implements a variety of tests for data containing many long panels, known as the large-N large-T case. Think of a long series on supermarket purchases for a large number of buyers. Or think of repeated visits to a website by the site's subscribers. Time series are said to be nonstationary when they have a mean or variance that varies over time. Some nonstationary time series are stationary if you first difference them.
Nonstationary time series tend to wander. Cointegration says that they wander together, meaning that there is a long-run equilibrium relationship among the series. And in Stata 15, we can now test for cointegration using the xtcointtest command. xtcointtest tests for the presence of this long-run cointegration relationship. Three tests are available: Kao, Pedroni, and Westerlund.