KernelSpace is where the kernel resides. It has full access to hardware and to all processes memory. UserSpace is where applications reside, they can't see the hardware, they can't even tell if other applications are running let alone interfere with them.
Most people think of Linux as being the full install. On behalf of RMS I'd like to remind everyone that a typical 'Linux' distro is composed of thousands of utilities that are NOT part of the linux kernel, many or which were written as part of the GNU project, BSD, X11, and various individual programmers who have chosen to licence their code under the GPL or BSDLicense or other Free software licence. The term 'Linux' specifically refers only to the kernel itself. OTOH while RMS would like you to refer to "GNU/Linux", it would really only be fair to say "GNU/BSD/X11,and_assorted_others/Linux" which is getting patently absurd, so most of us just say 'linux' even though we're aware that technically, linux is only the kernel..