Why to store a function parameter value in a class private variable?
The reason is that _Display will be used probably after its construction.

So you pass the byte during construction, and afterwards the value is available during the object's lifetime. 

In C you probably will do this by:


Passing the variable (byte DisplayType) in each function where the value is needed (you can use this way in C++ too but it's cumbersome in both C/C++ to pass the variable in all functions needed).
Storing it in a global variable (static for that .c file); this is the typically C method.


* Added explanation *

Such a variable is called class variables and are mostly made private. The reason is that other objects cannot change the value directly. The only way to change a variable is:


By initializing it in the class constructor (like in your example). 
Within the class itself (by any method).
By a typical Set method (like SetDisplayType). This method can check if the value passed is within a range, and there is only one entry point in this class to change it. 


To retrieve the value, typically a GetDisplayType method should be created which is public. The variable itself is private.