Something which is monochromatic has a single color. In physics, the word is used more specifically to refer to electromagnetic radiation of a single wavelength.
For an image, the term monochrome is essentially the same as black-and-white, but the monochrome may be preferred to indicate that combinations such as green-and-white, green-and-black, etc., are not excluded.
In computing, monochrome has two meanings: it can mean having only one color which is either on or off, or also allowing shades of that color. Thus it has the same ambiguity as the term black-and-white.
A monochrome computer display is capable of displaying only a single color, often green, amber, red or white, and often also shades of that color.
In the physical sense, no real source of electromagnetic radiation is purely monochromatic, since that would require a wave of infinite duration. Even sources such as lasers have some narrow range of wavelengths (known as the linewidth or bandwidth of the source) over which they operate.
The word monochromatic comes from the two Greek words mono (meaning "one"), and chroma (χρωμα, meaning "surface" or "the color of the skin").
See also: Monochrome BBS.