There is this little LED, right on the board of the Arduino, just above the TX/RX LEDs. According to the tutorial's wisdom, it is connected to Pin 13.
What I am curious about is, that if I open the Serial Monitor from IDE, that LED truns on, if I close the Serial Monitor, that LED turns off. Does this LED have a special role regarding the serial communications with Arduino?
that if I open the Serial Monitor from IDE, that LED truns on, if I close the Serial Monitor, that LED turns off
That is because the serial port is resetting the arduino. It is the boot loader that turns the LED on and off.
Sorry Mike, did you mean 'resetting'?
I noticed, as well, that as soon I close Serial Monitor, code on the Arduino stops working. Why is that?
did you mean 'resetting'?
Yes.
The auto reset on the arduino allows the synchronisation of the bootloader when loading code.
as soon I close Serial Monitor, code on the Arduino stops working.
No it just resets, so it will start again. What makes you think it is stopping?