Parent function are the simplest function possible of a "function family".
See: for quadratic functions y = ax² + bx + c where a ≠ 0 all the others can be, so the simplest quadratic function would be y = ax² + 0x + c, or y = ax², but if we say a = 1 and just let y be equal to x²? We have the simplest of all y = x²
The other one who do this is he's the simplest function possible of root functions.