[Solved] Explain how the following program works?

I hope that this explanations can give you some hints. By analyzing the code functions you should be able to figure out the rest.

VGA_WIDTH – width of the screen;
VGA_HEIGHT – height of the screen

x – horizontal position of the character on the screen

y – vertical position of the character on the screen

Since VGA card keeps all characters in a linear memory it has to use x, y,
VGA_WIDTH and VGA_WIDTH to calculate an index for its internal buffer to store a character at the proper memory location.

void terminal_initialize – this function initializes your terminal. It just puts spaces on the entire screen.

void terminal_putentryat(char c, uint8_t color, size_t x, size_t y)

puts a character c, on the screen at the location (x,y).

void terminal_putchar(char c) – it puts a character c, at the screen.

This function has terminal_column and terminal_row variables to track the current terminal column and row.