for wp-admin/

The left-hand navigation menu provides links to the administration screens in your WordPress application. You can expand or collapse navigation sections by clicking on the arrow that appears on the right side of each navigation item when you hover over it. You can also minimize the navigation menu to a narrow icon strip by clicking on the separator lines between navigation sections that end in double arrowheads; when minimized, the submenu items will be displayed on hover.

You can configure your dashboard by choosing which modules to display, how many columns to display them in, and where each module should be placed. You can hide/show modules and select the number of columns in the Screen Options tab. To rearrange the modules, drag and drop by clicking on the title bar of the selected module and releasing when you see a gray dotted-line box appear in the location you want to place the module. You can also expand or collapse each module by clicking once on the the module's title bar. In addition, some modules are configurable, and will show a "Configure" link in the title bar when you hover over it.
The modules on your Dashboard screen are:
Right Now - Displays a summary of the content on your site and identifies which theme and version of WordPress you are using.

Recent Comments - Shows the most recent comments on your posts (configurable, up to 30) and allows you to moderate them.
 
Incoming Links  - Shows links to your site found by Google Blog Search.
 
QuickPress - Allows you to create a new post and either publish it or save it as a draft. 

Recent Drafts - Displays links to the 5 most recent draft posts you've started.

WordPress Development Blog - Contains official news and announcements from WordPress.org to keep you informed.

Other WordPress News - Shows the feed from http://planet.wordpress.org. You can configure it to show a different feed of your choosing. 

Plugins - Features the most popular, newest, and recently updated plugins from the WordPress.org plugin repository.

For more information:
Codex - Dashboard [http://codex.wordpress.org/Dashboard_SubPanel]
Support Forums [http://wordpress.org/support/]

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for wp-admin/update-core.php
This screen lets you update to the latest version of WordPress as well as update your themes and plugins from the WordPress.org repository. When updates are available, the number of available updates will appear in a bubble on the left hand menu as a notification. It is very important to keep your WordPress installation up to date for security reasons, so when you see a number appear, make sure you take the time to update, which is an easy process.

Updating your WordPress installation is a simple one-click procedure; just click on the Update button when it says a new version is available. 

To upgrade themes or plugins from this screen, use the checkboxes to make your selection and click on the appropriate Update button. Check the box at the top of the Themes or Plugins section to select all and update them all at once.

For more information:
Codex [http://codex.wordpress.org/]
Support Forums [http://wordpress.org/support/]