Phone batteries store energy. They are typically rechargeable Lithium-Ion batteries. The capacity is the amount of energy that can be stored and is measured in mA (milliamps), e.g. 3000mA. Some batteries are removable by the user, but more commonly they are glued inside the phone and need to be replaced by a technician (with a heat gun and care). Typically phone manufacturers aim to have a battery as small as possible but last one day.
The Android Operating system monitors the battery health, temperature, and voltage. The battery health is either good, overheating, overvoltage, cold, a failure value, or dead. “Good” is the desired health. This means that no problem has been identified with the battery. Specifically, the battery subsystem has not triggered a condition that it determines to be a fault.
High battery temperatures are not good for your battery, make sure you don’t leave your phone in a hot place for long periods of time (like in your car all day or on top of hot electronic equipment). Also, beware of quick phone chargers as these can generate extra heat.
The Android Operating System has various levels of power saving operation (in Settings, e.g. Off, Mid or Max). This changes the usage of high power components like display brightness, maximum CPU speed, and background network usage. This can be helpful if you need to extend the battery use on a single charge. In my opinion, the highest power saving option is only useful in extending your battery duration in emergencies, as the adverse impact on phone functionality is high.
The battery charging rate is determined by the hardware (charger and phone). Fast charge apps seem to work by killing apps/ processes that are using battery (maybe even putting the phone in Airplane mode) – i.e. they don’t actually charge any faster, they just don’t use as much power while charging. ‘Fast charging’ is built into some hardware, e.g. Qualcomm Quick Charge or Adaptive fast charging – to use this you need a phone, cable and a charger that supports it (more information on Samsung Adaptive fast charging).