In Linux, Logical Volume Manager (LVM) is a device mapper target that provides logical volume management for the Linux kernel. LVM is used for the following purposes:
LVM can be considered as a thin software layer on top of the hard disks and partitions, which creates an abstraction of continuity and ease-of-use for managing hard drive replacement, repartitioning and backup.
(source: WikiPedia)

To view the free space of your volume group, or the physical storage, run vgdisplay. As you can see, I got 52GB in use and 170GB free.
root@scrat:~# vgdisplay
--- Volume group ---
VG Name scrat-vg
System ID
Format lvm2
Metadata Areas 1
Metadata Sequence No 5
VG Access read/write
VG Status resizable
MAX LV 0
Cur LV 3
Open LV 3
Max PV 0
Cur PV 1
Act PV 1
VG Size 222.82 GiB
PE Size 4.00 MiB
Total PE 57042
Alloc PE / Size 13436 / 52.48 GiB
Free PE / Size 43606 / <170.34 GiB
VG UUID e3grIy-rsTn-iUN6-Qpp2-wnnX-R2HP-s3BM7B
We can also see the logical volumes inside the volume group. This is the lvdisplay command. As you can see, the volume has a size of almost 9GB.
root@scrat:~# lvdisplay
--- Logical volume ---
LV Path /dev/scrat-vg/root
LV Name root
VG Name scrat-vg
LV UUID m5R02p-mx2h-gbTU-sWsv-n2n6-ov5b-Y8Y9f7
LV Write Access read/write
LV Creation host, time scrat, 2020-04-23 18:34:58 +0200
LV Status available
# open 1
LV Size 10.00 GiB
Current LE 2216
Segments 1
Allocation inherit
Read ahead sectors auto
- currently set to 256
Block device 254:1
You can resize the logical volume. You only change the partition size, not the formatting! The + is for the amount of data you want to add tothe volume. Without it's the total amount the volume has to become.
root@scrat:~# lvextend -L+5G /dev/scrat-vg/root
Rounding size to boundary between physical extents: 4.90 GiB
Size of logical volume centos/var changed from 10.00 GiB (1280 extents) to 15.00 GiB (2560 extents).
Logical volume var successfully resized
To let the filesystem grow, online, use for ext3/4:
resize2fs /dev/scrat-vg/root
For xfs based filesystems:
xfs_growfs /dev/scrat-vg/root