Purpose of LED indicator
This buildin LED is connected to an IO pin of the microcontroller on the Mega (most commonly pin 13, but might be different depending on the board). So the meaning depends on what the code on the Mega does with it.
When the board is reset (which happens on opening of serial connection), first the bootloader will run. It gives you a short blink on the buildin LED. After the bootloader finishes, your own code is in charge. Whatever you do in your code with pin 13 will be reflected on the LED. Here the meaning depends on you.