I'll try to address a few things that davenn passed on
I don't understand why the cathode of the capacitor
This is perhaps the first time I've heard anyone talk about the cathode of a capacitor outside discussions of the internal structure of polarised capacitors.
It's certainly not wrong, but applies only to polarised capacitors, and is a little tricky if you're talking about non-polarised electrolytic capacitors...
is connected to the base of a NPN transistor because the base is P-Type silicon so shouldn't it connect to a positive element?
You need to look at the voltage levels involved. The capacitor exists to isolate any DC bias difference between the input of this stage and the output of the following one. If you presume that there are several similar stages like this connected together to get higher gain, then the output of this stage would be connected to the input of another similar stage.
When the transistor is off, the output is neat the supply rail. When it is fully turned on, it is some fraction of a volt (more likely a volt or so) above 0V. The base of the transistor is essentially fixed at 0.7V. It is clear that the output voltage can be considerable more positive, and possibly never more negative than the base. On that basis, the positive end of the capacitor should be connected to the source of the input signal.
If the input signal was from a source that had a negative bias, then you would have the capacitor the other way around.
It should be "bias resistor". It applies a bias to that which will thus be "biased"
...Either that or it has a strong opinion.
However, when was it ever "not" a voltage?
There are several models of a transistor, but a simple one is that it is a variable resistor
with the resistance determined by the base current.
The load resistance forms a potential divider with the "resistance" of the transistor. As the transistor's resistance changes, the voltage on the mid point of the voltage divider varies.