This circuit is built around LM3647 an Universal Battery Charger, This Circuit is an untested design. It is based on application hints and was provided as an example to the user. This circuit gives a 12V DC from mains or battery and the battery is also charged when power resumes.
U1D monitors charge current and U1B monitors battery voltage these values are the feedback to charge controller U3. U1C drives Q2 to Control the charging process by switching in PWM. The LM7812 with a 2N6107 Current Booster Regulate the battery and mains DC to a 12V for powering the Product Circuits.
Portable electronics have got a big boost due to batteries like Li-Ion. Here is a decade old circuit to charge a large battery. It can be scaled up or down in power. It has current and voltage limit protections.