Error: " expected unqualified-id before 'int' ", array, argument, function,

In Standard C++ the size of an array must be a compile time constant. So when you wrote:

int size;
cin>> size;
int array[size][size]; //NOT STANDARD C++

The statement array[size][size]; is not standard c++.

Second when you wrote:

void display_current_array(array[size][size], int size){
//...
}

Note in the first parameter of the function display_current_array you have not specified the type of elements that the array holds. So this will result in the error you're getting.

Solution

A better way to avoid these complications is to use a dynamically sized container like std::vector as shown below:

#include <iostream>
#include <vector>

// a void function to display the vector after every moove
void display_current_array(const std::vector<std::vector<int>> &vec){//note the vector is passed by reference to avoid copying
  
    for(auto &row: vec)
    {
        for(auto &col: row)
        {
            std::cout << col ;
        }
        std::cout<<std::endl;
    }
}

int main(){
    int size;

    // ask the player to give a board size
    std::cout << "What is the size of your Hex Board ? ";
    std::cin>> size;

    // create the 2D STD::VECTOR with size rows and size columns to represent the board
    std::vector<std::vector<int>> vec(size, std::vector<int>(size));

    // the player will choose colors that we will store as an enum type
    enum colors {BLUE, RED};

    //NO NEED TO INITIALIZE EACH INDIVIDUAL CELL IN THE 2D VECTOR SINCE THEY ARE ALREADY INITIALIED TO 0

    display_current_array(vec);

}

Note that:

1. We don't need to pass size of the vector as an argument
2. the vector is passed by reference to avoid copying

The output of the above program can be seen here.