What's the Minibox?

It's the floating box in the upper right hand of your screen.

What are these links for?

Switching on and off a couple of site-wide features for your current browsing session.

Is it saved when I close my browser?

For a casual user, no. It is dependant upon the session, and it does not leave any cookies behind. However if you want to make a permanent setting (or more accurately, a default state when you log in) you can do so via your Account Settings.

Enabling this link will place additional player icons next to downloads, so rather than only having the download option - you also get the ability to open a player for the modules that are supported by the player. If a red 'X' appears next to modules, this indicates that the player does not support the file format of the module

Enabling the Detailed Module View makes the site display more information about the modules in the module listings and search results with the exceptions of the New Comments and New Additions lists.

If you are an artist, this setting will also affect the Manage my Modules area.