All items for your website have an Access Level setting. In the example below you can see the Access Level column in the Article Manager page. This column exists for menus, modules etc as well. You can restrict access to items by simply clicking on the green text in the 'Access Level' column, next to the item you wish to change. In the example below you would click on the word 'Public' next to an item. When you click on the word, it will change from 'Public' to 'Registered'. If you click it yet again, it will change from 'Registered' to 'Special'.
If you wish to hide an item so that it is only visible for members who log into your website, set it to 'Registered'. This is all you need to do.

What should you do if you don't want ALL of your members to see a particular item? There are two possible solutions to this. The first solution is to create a community type feature for your website, where each member has a more detailed profile and private messaging etc. You can use this to communicate with each member on a personal level.
Alternatively you could simply create an independent link and send it to one member. Only that one particular member will have the link and nobody else will know how to get to it, so it is in effect a private page. How do you do that? Go to Menus>Menu Manager and create a new menu called eg 'Private Pages' and save it. Then go to Menus>Private Pages and create a link by clicking on 'New' in the top right, choose type 'Article' and link it to the page you want to use. If you click on 'Apply' instead of 'Save' when you're finished, you'll see the 'Link' field change as below.

Copy the value in the 'Link' field, you'll need this. Append this value to your website address, eg our address is www.dotcomkiosk.com so in this example we'll need to add the link value to the end by copy and pasting it. Note the forward slash between the website address and the field value (in red below):
www.dotcomkiosk.com/index.php?option=com_content&view=article&id=558
Use the link you just created and send it to the person you wish to show it to. Nobody else will be able to see the page, because the steps above explain how to create an independent link, which is not shown anywhere on your website.