You are using LVM,the logical volume manager, this is great, do NOT change that ;)
Your Disk has 3 partitions, the third partition is your pysical volume, sudo pvs (physical volume show) will show you that.
This is part of a volume group (vg-ubuntu), which you can display by sudo vgs (volume group show).
On this volume group you have a logical volume, which you can display by sudo lvs (logical volume show).
On this logical volume you have your filesystem.
You can create a second logical volume by lvcreate -L SIZE -n LVNAME VOLUME_GROUP, eg.
lvcreate -L 20G -n data vg-ubuntu, then create a filesystem with
mkfs.ext4 /dev/vg-ubuntu/data.
You can extend your existing with lvextend -L +50G /dev/mapper/ubuntu--vg-ubuntu--lv, followed by extending the filesystem by resize2fs /dev/mapper/ubuntu--vg-ubuntu--lv.
You can also create snapshots of your logical volume if you have some room left in your volume group, so i would recommend to only increase your logical volume to how much space you really need, NOT to the full space available in your volume group.
Remember you can always increase your volume size as long as you have space in your volume group.
Have fun