Why can't I paste anything under the /usr/ folder?

Mallik is right. You don't own this directory, since it is a system-directory and not a user-directory, like /home/Username, where you can copy/paste files as you wish!

Please don't change the root permission of any system-directory permanently, since your system manages on its own and you can only break it that way. Instead open Terminal and use sudo before your command to copy cp, or move mv files/folders.

Put the folder you want to copy (I call it myNewTheme) on your desktop!

Your command should be as followed: (you need to replace the path/dir and name of the folder you want to copy/move):

sudo cp -r /home/Username/Desktop/myNewTheme /usr/share/kde4/apps/ksplash/Themes/

The -r stands for recursive, since it is a folder (parent), with sub-folders/files (children) and therefore recursion is mandatory!!

A regular/normal user usually will not have write access to /usr directory. You would need super user permissions to do so. Please login as root and you could do that.