Creating Background:

AndEngine lets us to create few different types of backgrounds without much effort, I will try to cover those most frequently used.

1. Colour Background.

private void createBackground()
{
    scene.setBackground(new Background(Color.RED));
}

In this example, whole screen will be filled with RED colour.

2. Parallax Background:

private void createBackground()
{
    ParallaxBackground background = new ParallaxBackground(0, 0, 0);
    background.attachParallaxEntity(new ParallaxEntity(0, new Sprite(0, 0, background_region, vbo)));
    scene.setBackground(background);
}

We created new ParallaxBackground, attached new ParallaxEntity (which is our background Sprite, in the top left corner [0x,0y]) 

3. Auto Parallax Background:

Auto Parallax Background is an extension class of the Parallax Background, it lets you to control parallax entities(ex. creating movable entities like clouds etc) but its bit stubborn and I recommend to use ParallaxLayer class shared by jaym.  It lets you to easily create cool effects without much troubles.