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The Visible, Visible in Render, and Selectable parameters determine whether or not you can see an object in your scene, and whether or not you can select the object.
The Visible parameter comes in handy for cases such as the following:
The Visible in Render parameter makes it possible to hide objects during rendering but still be visible in the scene as you are working. This is useful for things such as body handles and nodes you don't want to see in your scene but don't want to keep changing the opacity back and forth; and for body parts that are behind other objects and don't need to be visible.
For example, below is a hair style with body handles and glasses. The top body handle, the bottom center body handle, and the glasses were selected and Visible in Render set to Off. When rendered, those objects will not be rendered but when you return to the OpenGL view, they'll be visible again and ready to be adjusted as needed.
The Selectable parameter is helpful when you have spent a lot of time arranging your scene or posing a character and you want to prevent accidental changes from occurring. When the Selectable parameter is off, DAZ Studio does not allow any parameter changes to be made to the object.