Optimal Transport (OT) is a mathematical field used in many interesting and popular tasks, such as image segmentation, image restoration, computer vision, data analysis, etc., and in general, OT can be useful for those tasks involving a density distribution.

It provides you with the least effort requiring way to transform one distribution(shape) to another by essentially rearranging the mass(here probability).

The most classical example is given by the task of rearranging a sand pile to desired shape.

This also helps quantify a distance between probabilities which take into account their geometries. Distance is little if the mass has to be moved little to match the target and high if otherwise.