In a PoE system, power-source equipment (PSE) injects 56.5 V at a maximum current level of 350 mA onto a standard Ethernet LAN cable. Maximum power at the Ethernet switch is 15.4 W per PSE port.
However, due to cable losses, the maximum voltage and power available at powered-device (PD) equipment (phones, wireless access points, cameras, etc.) is 48 V and 12.95 W, respectively. Newer Ethernet switches include the PSE function internally, but a PSE product called a Midspan Hub can be used to insert PoE power in legacy installations. Legacy PDs can be powered by PoE splitters (or "pickers" or "taps"), which extract the power from a PoE LAN cable and pass it on to the PD via a short cable.
Why only 13 W? When the committee was established in 1999, VoIP phones were virtually the only application envisioned (although security cameras were already using proprietary power-over-LAN schemes and carrying as much as 1.5 A on CAT5 cables). For handset-phones, 13 W was plenty, and the committee based its current limitations on conservative cable data-sheet specifications.