Logical Volume Management (LVM) is a method of allocating space on mass-storage devices.
It can provide features superior to traditional partitioning schemes, such as concatenating, striping, or combining partitions, and resizing or moving partitions, potentially without rebooting.
Some related commands that will help alongside the LVM commands are:
lsblk blkid /dev/mapper/lg_name-lv_name

Displaying information:
pvdisplay vgdisplay lvdisplay lvs
Adding a new physical device to extend an existing Logical Volume:
pvcreate /dev/sdb vgextend vg_name /dev/sdb lvextend -L +5G /dev/mapper/lg_name-lv_name resize2fs /dev/mapper/lg_name-lv_name
Extending an existing Logical Volume to fill the entire Volume Group:
lvextend --resizefs -l +100%FREE /dev/mapper/lg_name-lv_name
Creating new Logical Volumes on a new Volume Group:
vgcreate vg2_name /dev/sdc lvcreate vg2_name -L 10G -n lv2_name mkfs.ext4 /dev/mapper/vg2_name-lv2_name lvcreate vg2_name -L 10G -n lv3_name mkfs.ext4 /dev/mapper/vg2_name-lv3_name
lvcreate /dev/mapper/vg2_name-lv3_name -L 5G -s -n lv3_snapshot mount /dev/mapper/vg2_name-lv3_snapshot /mount_point/ lvconvert --merge /dev/mapper/vg2_name-lv3_snapshot lvchange -an /dev/mapper/vg2_name-lv3_name lvchange -ay /dev/mapper/vg2_name-lv3_name
BONUS
Here is a quick step-by-step that should work on default Ubuntu installations that have LVM on the root volume.
df -h lsblk blkid /dev/mapper/ubuntu--vg-ubuntu--lv pvdisplay growpart /dev/vda 3 pvdisplay vgdisplay ubuntu-vg lvextend -l +100%FREE /dev/ubuntu-vg/ubuntu-lv lvdisplay /dev/ubuntu-vg/ubuntu-lv vgdisplay ubuntu-vg df -h resize2fs /dev/ubuntu-vg/ubuntu-lv df -h