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The KDE Menu is opened by clicking the blue
icon in the left corner of the desktop panel.
Starting with KDE 4.0, the menu has defaulted to the "kickoff style" shown below:

Kickoff has tabs for you favorite applications, all applications, computer resources such as discs and various options for logging off. Its precise appearance will vary based on your desktop theme.
Kickoff also offers such features as a menu search box, this allows you to search through the menus to find what you where looking for and the "computer" tab will show things such as removable discs allowing you to access them.
Prior to KDE 4.0 the menu looked like this:

As you can see, the "favorite" applications appear at the top of the menu and as a submenu¹, the applications make up the body of the menu and the leave options appear as a submenu. The computer menu is completely absent.
This menu is very similar to the Start menu included with Windows 95 and later

If you do not like the "Kickoff" menu, you can switch to the classic menu by right-clicking the
icon and selecting "Switch to Classic Menu Style".
If you want to go back to the Kickoff style, right click
and select "Switch to Kickoff Menu Style".
¹ The reasons for this are complicated; In KDE 3.x it was possible to alter the behavior of this area to show the statistically most used applications and the favorites where shown in a dedicated submenu. Unfortunately the "most-used" feature rarely yielded the desired results because it failed to take into account how people actually use computers.. This capability seems to have disappeared in KDE 4 but the area remains.