1. Eye button on the Timeline
This button appears in the timeline panel in the first column, on top, next to the lock button. If you click the top button all objects on the stage are hidden. To hide individual objects, click a radiobutton left of the object timeiine. A red cross will appear (see screenshot below). A full explanation of this and other timeline features and can be found in this article. Hiding an object on the stage has no effect whatsoever on the presence of that object when publishing (or previewing) the course: the object will be visible. What is the goal of this eye button? As you know (if you did read the article about the timeline), contrary to normal video timelines (included the Video Demo Timeline), a cptx slide will show all objects on the stage, whether they are scheduled to appear from the start or later on. That makes aligning a lot easier, but can also lead to a very crowded stage where objects are covering up other objects (except in the case of Fluid Boxes). To facilitate editing, it can be useful to hide some objects using this first Eye button.
This screenshot, taken from the game explained in 'Using the While loop' shows several hidden (on stage) objects and even a group. Since the topmost group still has one visible object (click box), its bounding box is visible on the stage. For the other group even the bounding box has disappeared.
There is one exception: you can also click the radio button left of the slide timeline. In that case the slide will be hidden (with all its content) and it will not appear when previewing/publishing. It is an alternative work flow for using the right click menu on slide(s) in the Filmstrip, option 'Hide Slide'. With both work flows you'll see a dimmed slide in the Filmstrip and an eye icon (not a button) as indicator.
Eye button in the Properties panel: Visibility in Output
If you want an object to be initially invisible in the published course, you need to click this button in the Properties panel (inspector) of that object, top left. It is almost the opposite button of the first because the object will not disappear on the stage at all. Why would you hide an object in a published course? Maybe because you'll want to make it visible later on. Example: you want to allow navigation to the Next slide only after certain actions have been performed by the learner (like clicking hotspots, or entering text in fields). Showing an object will be done with the command 'Show'. Making an object invisible by using this second Eye button can also be done on runtime by the action 'Hide' and that is often a better approach. Since you can show a hidden object, it means that the object is included in the published version which is not the case with a hidden slide. A hidden slide is not included in the published course.
Eye button in the Drag&Drop panel
When this button is set to 'active', and you did set up the Drag&Drop interactivity by defining the drag sources, the drop targets and the links for correct answers those three components are made visible: green rectangles for the drag sources, blue rectangles for the drop targets and blue arrows for the links. When you deactivate this eye icon, those indicators will disappear. Since it happens that Captivate deactivates that button without your consent, it is good to know how to make those indicators visible: click on the barred eye icon: