A switcher, also called a matrix router, is a device that routes input signals to certain outputs. It represents the most economical and traditional way of sending sources to one or more screens. There are switchers for all video formats, for example there are HDMI, DVI, VGA, etc. switchers, but not only that, there are also audio and other types of content switchers. Multiple sources can reach multiple screens but with the limitation that the switching is one to one, that is, only one source goes to each screen. With a switcher you cannot splice sources, or make a PiP (Picture in Picture), nor can you send more than one source per screen at a time.
A switcher is the way to save costs when you cannot invest in a Video Processor, which has more flexibility and versatility in its image handling.