The Koch Curve is created by using a seed shape to replace each straight line in the figure, which is a line. This seed shape is also referred to as the first generation, but I think to envision it as a seed makes its function clearer. You plant a seed and it grows. That is how it works with a fractal.

The Koch Snowflake uses the same seed shape as the Koch Curve. It is two sides of a triangle in the center of a straight line of which it is a third.

Instead of beginning with a straight line one begins with an equilateral triangle. Each side of the triangle is replaced with the seed shape, two sides of a triangle in the center of a straight line or which it is a third. Then each line segment of the snowflake is replaced with the seed shape.

A picture is worth a thousands words. Above is the progression of the creation of a Koch Snowflake. It begins with an equilateral triangle. Each straight line of the triangle is replaced with the seed shape. Then each new line is replaced with the seed shape. And on and on into infinity. (A fractal component.)