When you log in as an administrator, you get access to administration tools. At the top of the page, click on "Administration" to go into Administration screen. As you install and enable more plugins, your Administration menu would have more options. Only the standard installation is covered on this page. On the left menu, you would see the following links:

Statistics
Provides very basic statistics about site usage.

Site Administration
You are better off not changing anything here. These are the parameters you set when you installed elgg. Edit this page only if you know what you are doing.

User Administration
This section allows you to create, remove and find users.

Tool Administration
Elgg can be extended with plugins. Plugins provide additional functionality. For example, a plugin can provide calendar functionality. To install a plugin, you need to download and unzip it to the mod directory. Then refresh this page to see it in the list. Click on "Enable" to enable it. Now you can use calendar. To disable it, click on the "Disable" button next to the plugin.

System Diagnostics
Here you can generate a report of Elgg diagnostics

Log browser
Here you can see logs for all activity in Elgg.

Default profile widgets
This allows you to customize your view. Simply drag-and-drop items from the Widget gallery to Left widget, Middle widgets, or Right widget screens. This is how items would appear on your profile page.

Default dashboard widgets
This allows you to customize your dashboard. Simply drag-and-drop items from the Widget gallery to Left widget, Middle widgets, or Right widget screens. This is how items would appear on your dashboard.

There would be several other options based on your installation but these are more most important ones.