The mount point specifies at which location in the directory hierarchy a device or disk partition appears.
If you want to move /home to a new partition, you have to create a new partition for it, say /dev/sda4 and format it, e.g. with ext4. Creating partitions and formatting them can be comfortably done using e.g. gparted.
Then you have to copy the old contents to the new partition and modify /etc/fstab so /home points to the new partition. As root do something like this after having the partition created and formated. Again I assume /dev/sda4 for the partition, this is just an example and you have to use your real partition device:
$ mkdir /mnt/tmphome
$ mount /dev/sda4 /mnt/tmphome
$ cd /home/
$ find . -depth -print0 | cpio --null --sparse -pvd /mnt/tmphome/
$ umount /mnt/newhome
$ mv /home /old_home
$ mkdir /home
$ mount /dev/sda4 /home
Now check if your system is still working correctly. If it does, add a line like this to /etc/fstab:
/dev/sda4 /home ext4 defaults 1 2
and delete the backup in /old_home
if however you find that something went wrong, you can move back by not adding respectively removing the above line in /etc/fstab and doing as root
$ umount /home
$ rmdir /home
$ mv /old_home /home
This answer is inspired by the howto on http://embraceubuntu.com/2006/01/29/move-home-to-its-own-partition/
