"Tubbing" refers to housing your axolotl in a plastic container versus its permanent tank. Think a shoe box size or larger Rubbermaid/Tupperware container (just make sure it's food safe).
There are a number of reasons why you might wish to "tub" your axolotl. 1.) Medical treatment. 2.) Temporary housing while cycling it's larger more permanent tank. 3.) Quarantining before adding to an already established axolotl tank. 4.) Some owners like to tub while feeding to reduce waist in the tank. 5.) Health/wellness checks. 6.) To reduce stress while cleaning or changing tank decor.
When tubbing longer than a day, it requires once or twice daily full 100% water changes. The easiest way is to have two tubs, fill the empty one with cool, clean, dechlorinated water, and then dump and clean the soiled tub for the next water change. Let us know if you have any questions!