What is "ultralimit"

In mathematics, an ultralimit is a geometric construction that assigns to a sequence of metric spaces X a limiting metric space. The notion of an ultralimit captures the limiting behavior of finite configurations in the spaces X and uses an ultrafilter to avoid the process of repeatedly passing to subsequences to ensure convergence. An ultralimit is a generalization of the notion of Gromov-Hausdorff convergence of metric spaces.