Here's an example how charging system works on a car with combustion engine. Power from the alternator goes to the battery and then goes to the car systems. Alternator is connected to the battery all the time and it's charging it all the time when engine is on almost all cars. See the scheme below.
There's a special voltage regulator (modern cars have it built in into the alternator, old cars have it as a separate block) or ECU controls how much energy alternator should output by changing the output voltage. It checks the load (the load increases when you turn on high beam, stereo, window heaters all the lights, etc.) and „says“ to the alternator should it output more or less.
Some conditions may also affect alternator output. When hot thermal protection decreases alternator power output, when cold power output will be increased. On high RPMs alternator produces more power, on low RPMs it produces less.
So basically when the engine is off the voltage should be somewhere around 12.5 V (12-13 V). When the engine is on the voltage should be above 13 V and below 15.5 V. In some conditions even when the engine is on the voltage may drop below 13 V (really hot day, both A/C are on, stereo is on, lights are on, you're charging your laptop \ camera etc, you're driving really slooowly in a traffic jam).
So, low voltage when the engine is on isn't a good sign. If you have 12.5 V when driving - something is wrong. Also high voltage when the engine is on isn't a good sign. If you have more then 15.5 volts it's better to check your alternator.