With a VPS, I assume you do not have physical access to the machine, so the usual approach to resizing an in-use filesystem will not work (that would be to use a rescue cdrom).
In your listing, the /dev/mapper/vgxxx mountpoints are the way LVM volumes are mounted.
Tutorials on LVM are fairly easy to find. The problem if you have used all of your space is that shrinking the volume group for a live filesystem is said to be risky.
If you cannot empty out /home then one way to rescue your system would be like this:
- seeing that you have enough space one either
/usr or /var to hold both filesystems,
- you could copy all of
/var to a temporary directory in the /usr tree, and
- add a line in
/etc/fstab to use a bind-mount to make that copy of /var mounted as /var.
- comment-out the line in
/etc/fstab for the "old" /var, reboot
- You would lose "some" updates to
/var (between copying and rebooting), but the reboot would get the system back to normal operation.
- after rebooting, you could resize the (now-inactive) volume group where you have
/var, and
- add the space (physical volumes) to the group containing
/home.
Still, making a backup first is always a good idea.
Further reading:
Per comment, you actually have unused space on your disk, so in this instance it is not necessary to shrink one volume to make room for another. I will leave the work-around suggested since it could be useful advice.
However - when simply growing a logical volume, you have to add space to the volume and then resize the filesystem (the part that you care about). LVM is three layers (seen with pvdisplay, vgdisplay and lvdisplay). If pvdisplay does not reflect your 1Tb, you will have to use fdisk to add a partition to the set of physical volumes. Then update the volume group, adding the physical volume. Finally use resize2fs to increase the size of the filesystem inside that volume group. Here are some useful links:
vgsif you have free space in your volume group vg00? If so, this is very easy, and you don't need to worry about any shrinking stuff in Thomas Dickey's answer. – derobert Jan 13 '16 at 03:59