Layers and Objects i.e. Rectangles

What you are referring to are sub-layers. Every new object drawn gets its own sub-layer within the main layer. If you look at the screen shot below you'll notice that each sub-layer has a circle to the right of it. If you click on that circle (affectionately known as a "meatball") you can select only that sub-layer. Also notice that when a sub-layer is selected that a square appears at the far right. This allows you to move that sub-layer up or down within the layer and even onto another main layer. The purpose of this is so that within a drawing you can have something that is a single component of that drawing which is actually made up of several shapes all on one main layer but all of its shapes are accessible through the sub-layers. An example of this might be if you were drawing a house you might want all of the shapes that make up the door on a single layer with all of the door's panels accessible for selection on their individual sub-layers. You would then create new main layers for the windows, the roof, etc. each made up of many sub-layers.

The sub-layers are there as a possible way to make easy selections (and provide a way to change the arrangement of objects) within complicated objects. They do not preclude you from selecting any object in the document using the selection tools or changing the arrangement of object using menu items and key commands.

You've got the right idea.

When you create a new document, there is only one layer which is named Layer1 by default. At first there is nothing on that layer. As you add objects, all of them appear as sublayers under Layer 1.

If you want additional layers, you need to add them manually. All of the layer commands are in the flyout menu of the Layers panel.

You will find more information about layers at How to use layers in Illustrator