How do Ethernet Hard Drives work?

You would connect them to a router or a switch. Theoretically, any PC on that same internal LAN wold be able to access it. If it can see the router (wired or WiFi), it should be able to see that drive.

Now...do they all actually work that well? No. There are many, many reports of the actual connection being spotty.

They're a combination of an enclosure that includes an ethernet connector and controller, and a hard drive with its controller. You generally configure them (they have a built-in web-based config tool for this) to have an IP address for your network. So, yes, they plug into the router or switch.

For performance: these are secondary drives, not system drives. Even if you have gigabit internet, the built-in latencies slow you down way too much. They're fine for archive storage, or for streaming. To address USAF's comment, they *do* put themselves to sleep, and Windows likes to re-read directory structures. That can be slow when you connect back up. Win 10 seems to do better on this, tho.

If this is the only computer which needs to access the contents of the HDD, stop reading right now. Mounting the HDD inside the computer or via USB is almost always better than network attached storage (NAS) in this case.

If you have multiple computers which need to access the data, a NAS provides the advantage of 24/7 uptime with low power consumption, and independence from any computers (if the drive is connected to a computer via USB and shared, anyone trying to get data off that drive will be interrupted if Windows updates and requires a reboot).

In terms of speed, most 3.5" HDDs top out at about 150 MB/s peak, about 80-120 MB/s in real use (copying lots of large files).
2.5" HDDs top out at about 120 MB/s peak, 60-80 MB/s in real use.
SSDs top out at about 550 MB/s peak, 200-300 MB/s in real use.
Speeds are lower if you are accessing lots of small files (like copying a folder full of Word files).

USB 3.0 maxes out at just under 300 MB/s, with 150-200 MB/s being more typical
Gigabit ethernet maxes out at 125 MB/s, with 80-95 MB/s being more typical.
100bT ethernet (aka Fast ethernet) maxes out at 12.5 MB/s, with 10-11 MB/s being more typical.
802.11ac wireless maxes out at about 40 MB/s, with 20-30 MB/s being more typical.
USB 2.0 maxes out at about 35 MB/s, with 20-30 MB/s being more typical.
802.11n wireless maxes out at about 25 MB/s, with 11-15 MB/s being more typical.
802.11g wireless maxes out at about 3 MB/s, with 1-1.5 MB/s being more typical.

If that were all there was to it and you were accessing the files over Gigabit, then NASes would be great. Unfortunately, there's another variable. The interface between the HDD and the network makes a huge difference.

To get full Gigabit speeds usually requires an expensive NAS with a x86 processor. These will usually run you about $300-$500 minimum. $400-$1000 more typically. It's basically a small desktop at that point.

High-end ARM-based NASes are now hitting 80-100 MB/s over gigabit ethernet, usually in the $200-$300 price range.

Mid-tier ARM-based NASes get about 40-80 MB/s, and are usually in the $100-$200 price range.
A few routers with USB 3.0 ports can hit these speeds with a HDD plugged into the USB port.

Low-end ARM-based NASes usually get about 10-25 MB/s, and are usually in the $50-$100 price range.
Most routers with USB 3.0 ports get about this speed with a HDD plugged into the USB port.

Routers with USB 2.0 ports with a HDD plugged into USB are all over the place, with some getting 20-25 MB/s, others barely able to eek out 1-2 MB/s. I would suggest just avoiding them unless you already have one and don't need much speed.

So that's basically the trade-off. NASes are more expensive than USB 3.0 (especially if you want max Gigabit speeds) and typically slower. But they're more convenient if you want a file server available 24/7 and can reduce your electricity bill. The mid- and high-end NASes also have nifty functions, like a media server or download manager (you download a file or torrent and it automatically gets set to the NAS which does the downloading - you can turn off your main computer without interrupting the download or torrent).

Edit: One tenuous advantage of the NASes is that if your router supports a VPN server, you can login to your home network remotely and get your files off the NAS. This has saved my butt on several occasions (or at least saved me a 100 mile round trip drive), but I fix computers as a side job. I'm not sure how useful this would be for the typical user.

What's already been said. They have a built in web based OS configuration. You program them much like a router. Set up shared folders that are accessible from Windows, Mac, Android, etc...

Called a NAS or network accessed storage. They are great if you want to set up 2+ harddrives and have multiple TB of storage shared between devices in the house. That way each computer only needs a small SSD for the OS and installed programs. All storage is done on the NAS and each computer, smartphone, tablet, media player, gaming console, etc... can access the movies, music, pictures, files form the NAS.

Be aware though that the speed of them is hardware based. Just because it's on a gigabit network doesn't mean you'll get those speeds. A cheap $300 NAS will be 1/4th the speed of a $1200 NAS and a cheap NAS will get poor upload and download speeds. They work fine for streaming HD video and music though. Look for a NAS with more RAM and faster processors and check their UL/DL specs.

If you just want an external hard drive to plug direct to a computer and want it portable look for something like USB3 or eSATA.

The only difference between a NAS and an 'external hard drive'...ok, a couple. A NAS has much more configurability. A NAS is designed to use pretty much any hard drive or SSD. An external hard drive (such as a Western Digital MyBook) is pretty much a package...configuration is largely just setting an IP address, maybe setting a password. A NAS actually runs a small Linux OS, so it supports user accounts, defining shares, quotas...allll kinds of stuff. A MyBook or variant thereof, is intended to be a disk drive that just happens to be visible to anyone on your net.

Actually, let me clarify that. An external hard drive also includes drives with enclosures (and power supplies, typically), that connect to the PC, just *outside* the case. Ethernet is one; there's also eSata, USB, and Thunderbolt. Those 3 just make the drive visible to the one PC...UNLESS they're connected to a NAS, which can have the smarts to make them visible to anyone who can see the NAS.