HDMI splitters and HDMI distribution amplifiers are used if one HDMI source, e.g. a Blu-ray player, must be connected to several TVs or projectors at once. An HDMI splitter can thus ensure that the signal is distributed to all devices at the same time and without a loss of quality.
In shops, HDMI splitters are widely used as the same image is required to be shown on many TVs, but it can also be relevant in the home, e.g. if you wish to send the signal to both a TV and a projector, without having to change cables.
Remember to always use an extra HDMI cable from the splitter to the device concerned, as it is inserted in the HDMI connection. HDMI cables can be found here.