Strictly speaking residential infrared heating encompasses a lot of the heating that is commonly found in the home. It is simply the wavelength of the heat - much of the heat of the sun comes to us in the infrared range, and so does a lot of the heat from hot water filled radiators.
But what we usually mean when we talk of infrared heating in the home is specific electric-powered units that give off heat. These vary a lot, from ceramic or glass infrared light bulbs used for heating small spaces or animal hutches through to huge units that hang from chains in the roof and are usually used to heat massive workshops.
There are many units available specifically for the home, including purpose built shower units that give off very specifically directed hear. Because they use infrared, a radiative form of heating, they heat the person below the light and not the air all around - this means you do not need to heat the whole space to feel warm.
How the heater is set up varies too. You commonly find quartz glass heating elements, but this can be fragile and break easily. Some other designs use a metal sheath element. If you go with metal (sometimes in the form of a panel) you get toughness and no visible light given off. The positive side of quartz is that it is more efficient and heats up in a few seconds.