It's just an arbitrary label for people born in a certain period of history. These people generally have shared experiences that are different from the experiences of other generations.
> Who draws a line between generations and why?
Same people that draw a line between lemons and limes. It's sometimes a useful distinction so people remember it and use it.
> People do not stop being born, nor do they magically change because they supposedly belong to an imaginary generation.
There is no sharp dividing line between lemons and limes, either. Fruits in the citrus family can be crossbred with each other and you will end up with hybrids that cannot easily be classified as lemons or limes. There's no sharp line between "tall" and "short", or "white" and "gray". That's just the way names generally work, outside of fields like mathematics where you can use more precise definitions.