Power over Ethernet (PoE) (Wikipedia) is a set of standards or ad-hoc systems that enable power to be passed along an Ethernet data cable using twisted pairs.
In the smart home, this has the advantage of simplifying and reducing the number of cables that are required to each individual networked device. This is particularly useful for things like cameras, which may be quite distant and installed in difficult to reach locations.
IEEE 802.3af details a PoE technology designed to provide up to 15.4W of DC power (minimum 44Vdc and 350mA) to each device. Due to losses in the cable, only 12.95W is guaranteed to be available at the equipment to be powered.
a second standard, IEEE 802.3at, was introduced in 2009. Also known as 'PoE+', it can supply up to 25.5 W dc to the PD. The PSE provides 50 to 57 Vdc compared to 44 to 57 Vdc for PoE. Current for PoE+ is increased to 600 mA compared to the earlier technologys 350 mA.
It is possible to use a PoE injector, to insert power into a network cable for use with cameras, etc. The main advantage is that they can be used on existing networks, with no need to change the switch.
A PoE switch is an all-in-one box with no additional injectors required and the ports on it can be used to manage both network and power.
A PoE capable switch will have a set number of PoE enabled ports (i.e. not all of the ports may be PoE capable) and an overall power rating, which may mean that full power cannot be applied to all of the PoE capable ports. Sometimes it is better to use several switches in order to get more power ouput capability.
A PoE splitter is basically the opposite of an injector and allows the power to be separated and used at the remote end. Typically a splitter will also have circuitry to provide a fixed, regulated voltage at the remote end.
Whilst there are PoE standards, there is also a lot of ad-hoc solutions that utilise spare wires in Ethernet cables to deliver power over Ethernet (typically wire 7 & 8). These will often use non-standard voltages.