Copyrighted means there is a copyright and license protecting that. The license in the case of the Linux kernel is GPL (http://www.gnu.org/copyleft/gpl.html).
In a nutshell, you are allowed to modify the code in any way you wish. However, if you republishdistribute your modified code, you have to license it GPL and keep the credit to the original authors. Also, if you distribute compiled versions of the modified source, you have to distribute that modified source code.
The kernel's license is a so called "copyleft", you do what you want but you have to let others do the same to your modifications.
PS: this is a very simple explanation, for more information and details see the above link.