In cycling, a ride's Training Stress Score is a function of that ride's duration, average power and the intensity of the ride relative to the rider's capability. This Slowtwitch article provides a good overview on how intensity and TSS is calculated on a bike.
However, having TSS values for other sports allows a multisport athelete to take into consideration the physiological cost of activities in different sports. This is achieved by ensuring, say, 50 TSS on the bike "counts" the same as a 50 TSS run.
This can be used to simply determine the length, intensity and scheduling of an athletes next workout (to ensure adequate recovery) regardless of the combination of sports, or to identify the athlete's long-term tolerance to—and targets for—training load using metrics such as Chronic Training Load.
To make this possible when using Strava, I wrote a Chrome extension that estimates the TSS score of a run from its Grade Adjusted Pace distribution:
The "TSS (estimated)" value is calculated by the extension.
Source code is available. If you found this Strava extension useful, you might like my extensions to quickly switch between metric and imperial units or to change the default comparison filter.