Shadows are caused because light travels in straight lines. You may not normally notice this, but if you look at tree trunks on an evening, when the Sun is shining low in the sky, you will see the dark shape of the trunk stretched out on the ground in the direction facing away from the Sun.
If you stand or run by a wall when the Sun is low in the sky you will also see shadows.
The darker areas are there because the main light is coming from one place, and trees, your bodies and any other objects block out the sunlight. So a shadow is a place where there is less light. (There will normally be some light because light is being bounced off of other surfaces, and that will reach the area behind where you might be standing.)
If you try the same experiment at night, and use a torch instead of the Sun, the shadow will be completely black because the torch beam is smaller, and light from it will not bounce from other objects.
When the Moon goes between the Earth and the Sun, you will get a shadow of the Moon on the Earth. We call this an eclipse.