For example;
Suppose the gate requires 8.4V and 0V to turn PMOS on and off.
And consider control this PMOS with an Arduino running at 3.3V.
Arduino can't output 8.4V and even can't connect a gate pulled up to 8.4V.
(3.3V Arduino should only be connected to voltages up to 3.3V)
The NPN transistor responsible for level shifting begins to flow the base current at a voltage exceeding 0.7V.
The transistor turns on when the base current flows.
hFE (transistor's parameter) times the base current flows from the collector to the emitter.
(There is a resistor in the circuit to prevent excessive base current from flowing from the Arduino port.)
Unlike the Arduino port, the NPN transistor can apply up to the collector-emitter voltage listed in the datasheets.
That is, you can turn the 8.4V voltage on and off.
As a result, the Arduino outputs only a 3.3V signal, but uses NPN transistor to generate an 8.4V PMOS gate signal.
This is a level shift. 
(Well... If for true understanding, more detailed explanation such as PMOS gate pull-up, Vce (sat) of NPN transistor, andmore... required.)
I'm not an English speaker, so it's hard to write here, so I'm sorry, but please look for more websites. 
I think there are many good instruction videos about BJT and MOSFETs.