Another way of looking at it is that they save cable runs, not ports. If you've already got a router and a long 100BaseT cable to a PC, and you want to add a second PC, you can install a splitter on each end of the cable, connecting to two router ports, and the two PCs.

As a diagram:

Old:

 _________ Cat5
| 1|===================[PC]
| 2|
| Router 3|
| 4|
|_________|

New:

 _________ Cat5
| 1|---[splitter]=================[splitter]------[PC]
| 2|------/ |
| Router 3| --------[New PC]
| 4|
|_________|

I've only ever seen these splitters sold in pairs, for precisely this reason. To use them singly requires customised cables at the other end. That's certainly possible, but if you've got the kit to do that, it's probably easier to do the job properly and run a second cable. If you're starting from scratch, run enough cables in the first place (in my house I run two cables if I think I need one).

Ethernet splitters are not mini-hubs.

They are specifically designed to split a single connection with four twisted pairs into two connections with two distinct twisted pairs.

Read this write up here for the basics:

100BASE-T requires only two twisted pairs. So basically half of a Cat 5e cable. Just four out of the eight available wires. So if we’re only using half of the wires in the cable, couldn’t we make one cable act as two cables? Why yes! Yes we can! And that’s exactly what an ethernet splitter does!

So basically an Ethernet Y-splitter will give you two 100Base-T or 10Base-T connections from a 1000Base-T connection. Most ethernet wiring setups have four twisted pairs even if they are not needed for most uses. Thus why Y-splitters exist.

I have tried splitting the cables that go into the router with a Y and it does not work.

Are you sure you are using a router and not a plain modem with a single Ethernet connection? If this is a plain modem with one Ethernet port then a Y-splitter will just confuse the connection. And if your ISP tracks MAC addresses, then adding a Y-splitter will only make your ISP think there is something wrong or broken with your network.

You are much better off hooking up a real router to your modem than using a Y-splitter.

When you find yourself in the situation where you run out of cable drops, you can install one of these splitters (also somethimes called "RJ45 Cable Economisers") between one port on your patch panel and two on your switch. You then install a second one at the single RJ45 wall outlet (coming from the single port on the patch panel) and then connect two devices to it.

What I think a lot of people misunderstand with these things is that they don't give you additional ethernet ports. They allow you to multiplex a pair of ethernet connections across a single cable drop.

You need two because you have to mux at one end and demux at the other. You plug two ethernet sources (e.g. ports on a switch) into one of these and connect it to a single cable run. You connect the other unit to the other end of that cable run and then connect two devices (e.g. computers) to it.

It works by using unused pairs in the cable run to run a second connection. A device like this is useful when it is impractical to run a new cable from the device to the router (for example, when the existing cabling is in a wall and/or a new cable run would need to penetrate walls and floors).

These devices are not suitable for Gigabit ethernet because that uses all 8 wires within the network cable, leaving none spare. They are suitable for use with 10 or 100 ethernet however because they only use 4 of the 8 wires.

It's not a "splitter" per se, and shouldn't be marketed as one. It would be better to call it a "cable sharer".

From Wikipedia:

Shared cable

10BASE-T and 100BASE-TX require only two pairs (pins 1–2, 3–6) to operate. Since common category 5 cable has four pairs, it is possible to use the spare pairs (pins 4–5, 7–8) in 10- and 100-Mbit/s configurations for other purposes. The spare pairs may be used for power over Ethernet (PoE), for two plain old telephone service (POTS) lines, or for a second 10BASE-T or 100BASE-TX connection. In practice, great care must be taken to separate these pairs as 10/100-Mbit/s Ethernet equipment electrically terminate the unused pins.[citation needed] Shared cable is not an option for Gigabit Ethernet as 1000BASE-T requires all four pairs to operate.

Ethernet uses pins 1, 2, 3 and 6 because 4 and 5 would often be used for telephone services - a "6 pin, 2 connected" phone plug wired up to RJ11 fits into the RJ45 ethernet socket and makes contact with pins 4 and 5. By splitting ethernet up in this way one set of cabling in an office suite could support a shared use of the cable in the wall, which had 8 wires. Other ways of sharing and achieving multiple use of the wire were established too; some devices use the unused 4, 5, 7 and 8 for power, which means a single wire/plug/socket arrangement can both power a device and get data out of it.

Cable sharing devices like this Y device you have are another application of sharing the 8 core wire in the wall into two 4-wire plugs; you connect the single end of the Y into the wall, and the double end of the Y into two ports on your device (such as a router). At the other end you can connect two different ethernet devices into the double end of the Y and the single end of the Y again to the wall. After you have done this, your laptop is, for example, getting its internet over the orange pair and green pair set of wires inside the cable in the wall, and your desktop PC is getting its internet over the brown and blue pair. You have shared the use of the cable in the wall and made use of the formerly unused wires.

As other answers have pointed out, this is really only good for 100 megabits. If the cable in the wall supports gigabit and you want gigabit to both your laptop and desktop pc in the office, down to the router in the kitchen, then you buy a gigabit switch and put it in the office. You connect both computers to the switch then connect the switch, via the cable in the wall, to the router in the kitchen. Now everyone in the office has gigabit of some form. This is an electronic "sharing" of the ethernet network between the two computers in the office, versus a Y sharer, which achieves a physical sharing. The switch will always be the better route because of the number of devices it can support

Another use I've seen for passive Ethernet splitters is to use a network sniffer when you otherwise can't use a switch's mirror port (which exactly copies traffic from one or more other switch ports) and you don't have a hub (or similar) handy.

You put it inline between two devices and connect to a third device, where you're running Wireshark or another tool to capture the traffic.

If you're not running gigabit, this method can only see half of the traffic. Why half? Because the network card can only physically receive on one pair at once (for fast ethernet) and there are two pairs, one each for TX and RX in the source.

For example, Great Scott Gadgets makes the Throwing Star LAN Tap which allows you to choose which pairs you're connected to.

I looked up "Ethernet splitters" on Amazon, and the various descriptions state:

• 
  

  NOTE: Don't support 2 computers that connect to the internet simultaneously, ONLY 1 output port is working.

  
  
  

  This RJ45 Ethernet Splitter is not a switch so that it can not implement 2 computers sharing the internet at the same time.

  
  
  

  Application: When you often use a laptop in 2 different fixed position, using this RJ45 splitter, you don't have to worry about no Internet in your rooms.

  
  




• 
  

  This Adapter Advantage Design: A notebook in two different fixed position often back and forth use, this is a very trouble, the network cable to lead to broken, this rj45 1 to 2 ways RJ45 ethernet splitter help you do not have to pull back and forth cable. NOTE: This Ethernet splitter allows two computers to share one Ethernet line ONE AT A TIME, but it doesn't support both computer to connect onto the internet simultaneously

  
  
  

  Expand one RJ 45 outlet into two, standard 8P8C design. Please noted that only One port could be used at one time

  
  




• 
  

  ONLY ONE Female Port Workable At A time

  
  
  

  NOTE: This Ethernet splitter allows two computers to share one Ethernet line ONE AT A TIME, but it doesn't support both computer to connect onto the internet simultaneously

  
  




• 
  

  RJ45 Ethernet Network Splitter could help to split one network cable to 2 port output, that's convenient to take turns to use different computers. (Please note that cannot support using two cables at the same time)

  
  

You get the gist...