monochromatic radiation

Monochromatic means one colour. Ordinary white light is a mixture of every colour; a laser pointer is nearly one pure colour. X-rays come in colours too — the colour is just the wavelength — and diffraction works cleanly only when the beam is close to one pure X-ray colour. If many wavelengths hit the crystal at once, each one satisfies Bragg's law at a slightly different angle, and the sharp peaks smear into a mush.

You start from the raw tube output, which is white radiation: the broad bremsstrahlung continuum plus the sharp characteristic lines. To make it monochromatic you trim away everything except the strong K-alpha. Two common tricks do this. A thin metal foil filter (for copper, nickel) is chosen so its absorption edge sits just above the K-alpha energy and just below the K-beta energy, so it swallows the K-beta while letting K-alpha through. Better still, a crystal monochromator uses a good single crystal set at the exact Bragg angle for K-alpha, so only that wavelength is diffracted into the beam and everything else is thrown away.

Powder and most single-crystal methods assume monochromatic radiation, so that each plane spacing d gives exactly one measurable angle. (The opposite choice, deliberately using white radiation, is the Laue method: a fixed single crystal picks its own wavelength for each spot.) One honest caveat: even a filtered lab beam is not perfectly monochromatic — it still carries the K-alpha-1/K-alpha-2 doublet, so true single-wavelength work needs a monochromator that selects K-alpha-1 alone.