The triple rinse method is a classic rule for the cleaning out of laboratory equipment and containers destined for trash or recycling. In fact, at a former job of mine we had stickers that said "triple rinsed" that had to be placed on all solvent and reagent bottles before they could be put in a recycling bin otherwise they would not be picked up.
The triple rinse method is designed to minimize the exposure of custodial and waste management personnel to potentially dangerous chemicals or biological residues. Laboratories do not want people who handle trash or recycling to be exposed to anything dangerous, so all equipment and containers like test tubes or chemical containers are triple rinsed to remove all traces of hazardous chemicals. The rinse liquid is then placed into a hazardous waste container where it will be handled by appropriately trained personnel. The most important thing here is that the appropriate solvent is used for rinsing the appropriate container. Water can be used but it will not do any good for cleaning a container containing chemicals that are not water soluble. So some level of thought must be put into choosing the proper rinse solvent. Some common rinse solvents are acetone and methanol because they are not dangerous to handle properly and they dissolve both aqueous and non-aqueous materials.