This is an important method for staining bacteria; it was developed by Hans Christian Gram (a Danish scientist) in 1884.
The bacteria are placed as a smear on a slide, then air-dried, then stained first with crystal violet dye and then with Gram's iodine, then washed with 95% ethanol, flooded with safranin or fuchsin (red dyes) and air-dried again. If the bacteria retain the purple-blue stain on their cell walls, they're classified as Gram-positive; if they don't retain the crystal violet but take the red counterstain, they're Gram-negative.
This classification is important because the reaction to Gram stain correlates in many cases with the bacteria's vulnerability to certain antibiotics. The process only takes a few minutes, making it ideal for medical clinics.
If a clinician considers data from the Gram stain along with his/her medical examination of a sick patient, the clinician can get a pretty good idea of the pathogen that is infecting the patient and then start a regimen of antibiotics. In a clinical setting, the Gram stain is followed up with a bacterial culture (which takes three to six days to complete).
From the science dictionary at http://biotech.icmb.utexas.edu/