Stencil-strange blue icon?
 

I've attached a screenshot of some strange behavior.

I recently created a group of objects and was putting it into my stencil when I noticed upon pasting in the group of objects a strange blue icon appeared in the top right.

Let me be clear, my objects still function the way I would assume they should, but I am confused as to what this icon is supposed represent to me.

It means that there's a note attached to the object. (Or, strictly speaking, that its Note property has content.) The visibility of icons for special properties is controlled individually in the Extras section of the View menu and globally by the Extras button in the toolbar.

The icon shows up for a group if any object in it has a note or if the group itself does.