In gardening and horticulture, puddling is used to refer to a set of related actions used to keep plants healthy during transplantation.
In the most traditional usage of the term, one mixes up a slurry of water and fertilizer to coat a plant's roots. Historically this mix was made using manure, but these days one is more likely to use loam or potting soil. Some recipes call for additional ingredients; for example, if one is using cow patties, it is recommended that you add in some clay as a thickening agent. The goal is to have a thick mud that can thoroughly coat the plant's roots.
This sort of puddling can be done either when taking the plant out of the ground, in which case the goal is to have the mud dry onto the roots and protect the fine root hairs during transportation, or it may be done just before planting, in which case the goal is to 'wake up' the roots, and provide a convenient source of water and fertilizer. Puddling both before transportation and before planting is best.
Some modern gardeners have expanded on the traditional usage, and use puddling to refer to the practice of pouring water into the planting hole before inserting a seedling, to allow the water to seep down into the soil that the roots will be expanding into. This both encourages the roots to grow downwards quickly, and provides a lasting patch of water directly under the plant that will protect them from dry spells.
Perhaps to help with clarity, people usually speak of puddling, but will still conjugate the word to into puddle/to puddle as needed. This system does not do as much to avoid confusion as one might hope.