How can enabled WiFi save battery?
It saves battery... sort of. Please note, that this answer is based on this article.

Leaving it on is only good if you are connected to WiFi, as using WiFi is less power hungry than using 2/3/4G. So keeping WiFi on means that you use the less power hungry communication method. However, if you're sat in the middle of nowhere with the WiFi on, it will drain the extra power as you would expect.