Mac OS X can automatically arrange the icons on your desktop by their name, type and several other factors. If you are not careful when exploring the desktop preferences on your Mac, it is possible to accidentally configure the Mac to automatically arrange the desktop icons. Once this is done, it is no longer possible to move the icons unless automatic arranging is turned off.
Right-click in an open area of the desktop or hold the "Ctrl" key while clicking if you have a single-button mouse. Click "Show View Options" to display the view options for the desktop.
Remove the check from the box labeled "Keep arranged by". This restores the ability to move icons where you would like on the Mac desktop.
Remove the check from the box labeled "Snap to grid" if you prefer not to have the Mac automatically arrange your icons in a perfect grid.
Close the "View Options" window to save your changes.