Galvanic skin response sensors measure electrical connectivity of the skin. When internal or external forces cause arousal — of any kind — the skin becomes a better conductor of electricity. Essentially, when you start to sweat, either from exercise or something else, the band will be able to monitor that.
Detecting when someone is sweating gives the software more information about what a user is doing, which allows for better health tracking. Being able to correlate the level of activity with a different source than just gravity from the accelerometer, allows these programs to take on a more trainer-like role — recommending specific exercises and levels of exertion.