These discussions are rather advanced in my opinion, as you were asking about fundamentals that i gather from your follow up questions that you have not yet understood. This is not strange att all considering that no one here seems to want to just Keep it simple, so i thought i'd give it a go. DO Keep in mind that this is quite a bit simplified;
The 10k resistor between B and C allways delivers current to node B. No matter what. But when the BJT turns on and provides a path from B to ground you can more or less view the BJT as a low-value resistor, as it has a very much lower resistance than 10kOhm This means that you now have 2 resistances in series between your 8 volts and ground. (From C to B to GND).
As you may know, 2 resistances in series between a voltage source and GND is what we call a resistive voltage divider (IF you don't know what this is you should Google it, it is a simple concept) When the resistance closest to ground is much lower than the one closest to your voltage source, the voltage between the resistances (in this case at point B) will be closer to GND (0v). And reversely if the resistance closer to the voltage source is the smaller one, then the voltage in between them would be closer to the voltage source (8v). This is what causes the voltage to drop at the MOS gate even thought current is still flowing from C to B through the 10k resistor.
And like others have pointed out earlier, a BJT base always need to be driven through a resistor as the BJT's internal resistance from base to emitter is so low you can basically call it a short circuit. What they have not pointed out though, is that while this would destroy your BJT, wich is really cheap, it would most likely also destroy your Arduino as the short circuit current through the BJT is drawn directly from your Arduino, and is much higher than the 20 or so milliamps that an Arduino pin can provide.