You undoubtedly have some processes that are using files in your home directory. All your processes probably have it as their working directory, for example. Your session manager may be logging to
~/.xsession-errors, and so on.
If you've already done the move
When you moved your home directory to a different filesystem, you copied the files and removed the old ones. But you can't make running processes switch to the new files (not unless they have a feature to do that).
You'll need to log out and back in. When you log in now, the processes will be using your new home directory.
You can see which processes are still using your old home directory (or anything else on the home filesystem) by running
fuser /home or
lsof /home. Once you kill these processes, you'll be able to unmount
/home. You can use
fuser -k /home to kill them all (carefully check what they are before doing this!).
Better way to do the move
Ideally, you should move your home directory while not logged in, because your running processes might want to save data (e.g. saving your current session) and some will use the file that they already have open. You can do the move by logging in on a text console (Ctrl+Alt+F1) and logging in as root (make sure you have a root password configured). Move the content of
/home to a new directory, then unmount the empty filesystem and move the directories around:
mv /home/* /home.new/
mv /home.new /home
Or you can move the
mount --move /home /home.old
mv /home.old/* /home/