Monochromatic means sticking with one main color in a space and using different saturation levels of that color throughout. If you use purple, as an example, you could have lavender walls, eggplant chairs, an area rug with a gray-purple base, and so on.
Designing with a monochromatic color scheme seems easy, but is actually quite difficult as you are limited in what colors to draw from and are challenged to create visual interest and focal points when all the colors are from the same family.
One trick when working with a monochromatic color scheme is to add texture and pattern because they will pop out in a sea of similarly colored elements. Another trick to keep in mind is to stray somewhat in whatever color you are using in the space. This means to use a little bit of yellow-green and blue-greens in a green based palette.
The real key to a monochromatic color scheme is variety, so make sure to mix up the patterns, textures and saturation of the color you decide to go with!