The difference between Factor and Image: How can I combine them? I do not understand here what is the difference between Fact and Image:

Inputs
Factor
Controls the amount of influence the node exerts on the output image.
Image
The background image. The image size and resolution sets the dimensions of the output image.

How can I combine those two: Image and Fact ?
It is easier to understand if you use a black and white image to combine the elements.
This black and white image has two values: 0 means Black, and 1 means White.

The Factor input determines how two other elements in a node are combined:
Whatever is black will be the color of the Top image socket,
Whatever is white will be the image connected to the Bottom socket.

All other values between 0 and 1 (different tones of gray) in the Factor image, will result in a mix between the two values.