It's allowing water to drip into a container to gently acclimate the fish to your water conditions. People use airline with knots tied into it but I use IV tubing to do it.
Basically, whatever method you choose to drip the water into the container, you allow the water in the container to double in volume, dump half of it out, and then allow it to double in volume again. It's usually fine at the second doubling but you can keep going as long as you want.
"The simplest explanation for some phenomenon is more likely to be accurate than more complicated explanations." -Occam's razor