LEDE on embeded devices with low flash it uses two filesystems.
one is SquashFs, that allow to put tight all the ROM part, that is basically the firmware.
and when it boot for first time it put the initial configuration files on OverlayFS, this is the freespace portion of the flash...
usually you have 8mb of flash, 3.8mb is ROM, and the rest if available for OverlayFS.
OverlayFS as the name indicate is a "overlay" is on-top of the ROM filesystem, if you try to change a file existing in ROM, it will created an entry with that same file on the same path on Overlay in "upper" location.
if delete that file it wil be set a special flag indicating that the file does not exist, (overlay will hide the existence of the file in ROM)... if you delete a file from the upper it will bring back again the ROM version of the file.
mtdblock3 it points to the 3rd "partition" of the mtd, imagine that is like a partition on a hardrive, but just in flash, usually there is the ROM if I am not wrong.
/mnt is commonly by-choice location to mount filesystems (additional to the root one) like USB drive, etc...
extroot is the term for define that the system will use an external root filesystem instead of the bootloader defined one, OpenWRT and LEDE boots to a main ROM with a root filesystem, and in the process it look for a configured extroot (external root) on the fstab table or config file, as the system reads from /overlay and not directly from ROM, then the fstab entry it says /overlay on path.
USB drivers are needed, on LEDE, the system is so so tight and small some things like usb drivers (for the hardware part) and block storage (software part) both are needed to be installed to be able to set up correctly the extroot.
opkg saves it files on /overlay... as well al changes done to any file on the system. (ROM as the name intends is Read Only Memory, the only way to modify the ROM is that you build a new image for the device and flash/sysupgrade it again (overlayFS part will be copied to RAM temporary in order to re-adjust the usage of that freespace location)
please tell me what are your other "storage-related" terms that you need help about.
If you only need some space just for saving file you should mount additional USB stick like you already do, in /opt or even better in the common choice location of /mnt... you create your mount point there, example /mnt/usb-stick
if you need to install more packages and you don't have enough space you NEED to use extroot.
the tar command that you describe is very common, we use tar because it preserves well filesystem metadata like dates, permissions, etc....
Basically the process of extroot explained is this:
You should put and storage location like a usb drive...
use dmesg and logread to see if it was detected, install usb and block storage packages, install ext4 or f2fs packages.
set up your partitions on the usb drive, usually one uses 2 or 3... one for extroot, one for swap (if it is needed) and the rest for data storage not related to the system (example your YAMon statistics crap)
depending on your need you could use 100-500mb for system, that would be more than necesary since even if you installl a lot of packages you never gonna consume more than that.
you format your extroot partition, mount temporary and perform the tar command and unmount...
set up fstab mount entry (you could test it rebooting )... if it works well, change the mount point path to /overlay.
when you reboot you should be able to see more free space on the device when running
Hope it clarifies a little more the info about.