NAS refers to data storage devices connected over the network rather directly to your computer with an interface like USB, firewire or thunderbolt.

They were primarily stand alone devices with a network connection and disk array.

More recently wireless routers have added USB ports for connecting hard drives to serve a similar purpose.
They were originally very slow, but as of about 2015 with USB 3.0 and faster processers in routers they have become more popular.

The advantage of NAS storage is it can be located away from your computer without a special connection (assuming you are already connected to the network and they can be shared by multiple users.

HDD - Hard Disk Drive
NAS - Network Attached Storage
RAID - Redundant array of independent disks
SMB - Small & Medium Business
SOHO - Small Office Home Office
SSD - Solid State Disk