I built a Temple and researched Theology, and now I have a "Religion" tab. The only button in that tab I see right now is Praise the Sun. When I click it, it converts my faith to total faith. What is the benefit of doing that?
Faith, on its own, can't be used for anything at all without converting at least some of it into total faith on the religion screen. As you Praise the Sun, you'll unlock various upgrades on the Religion screen, many of which get stronger the more faith you convert.
You can distinguish fluid faith, which is the faith that you can max out and that is generated by priests and temples, and crystallised faith, which is what you get when you convert from fluid faith via Praise the Sun.
When you have 150 crytallised faith, you unlock the opportunity to get the Solar Chant mystery, which will then cost 100 fluid faith to actually obtain. Later you can unlock and gain other mysteries.