Drip acclimation is typically used when introducing sensitive fish to a new aquarium.  The "drip" of water from the new aquarium allows the fish to slowly adapt to the parameters of its new environment.
Typically, drip acclimation works like this:

• Put the fish and the water it was transported in into a bucket or bowl
• Add a small amount of a slime coat/ammonia detox like Prime to the water
• Place the container next to the new aquarium
• Place one end of an air hose (typical aquarium grade air hose) into the aquarium, and create a syphon
• Place the other end of the hose into the bowl
• Adjust the rate of flow by pinching the hose with a clamp or by using an air flow valve to 2 to 3 drips per second
• Allow the water level to roughly double, then remove half of the water in the container
• Allow the water level to double again, then move the fish into the new aquarium

The method does take some time, but it is by far the least stressful method of introducing a new fish, and an outright requirement for most sensitive fish.