'Umounting' means untying the file system (on the partition) from the rest of
hierarchy of files. For instance, when you plug your USB key while Trisquel
is running, its file system is automatically mounted (in a directory in
/media). When you "eject" it, 'umount' is called. Of course, the data are not
lost (actually, using 'umount' allows to ensure that all data were written
before actually unplugging the key).
It is useless to backup the system (it can be easily reinstalled). Focus on
your data (i.e., on /home). You can move them to another partition (on
another disk or even on the same disk, a partition that would not be touched
by parted). That said, you can live dangerously if you wish: the backup only
is a precaution (imagine, for instance, a blackout). GParted lists what it
will do before actually doing it: just check that you have not inadvertently
asked for formatting a partition!
GParted is pretty intuitive to use (and it is tedious to explain stuffs to do
with a GUI). Do not worry: you will figure out.
