"Pollarding trees" means cutting them back nearly to the trunk, so as to produce a dense mass of branches. It is sometimes done today for aesthetic purposes and/or to keep a beloved tree from outgrowing its bounds, necessitating removal. But traditionally, it was done for other reasons: The cut branches were either fed to livestock (fodder), burned as fuel or used to make things.
Pollarding begins on young trees, and the process is repeated throughout the life of the tree (meaning that, if you decide that this is something that you would like to subject your trees to, be prepared to undertake significant maintenance).
Only certain types of trees are suited to pollarding (when it is being done for aesthetic purposes). Here are some of those types, according to the Royal Horticultural Society:
Topping Versus Pollarding: Superficially Similar, but Different Operations
Now that you know the definition of "pollarding," you can distinguish it from "topping," which is another term used in arboriculture. But here is the difference between the two words: Whereas the former is done with design in mind, the latter is done out of expediency.
Topping means cutting older trees down almost to the top of the trunk. Topping trees is sometimes used as a less expensive alternative to their full removal, which can be quite costly in the case of large old trees. It is done not with an eye to what is best for the tree, but because the homeowner is in a pinch. Some types of trees may die after topping, but this fact often holds little importance to the homeowner, who may actually be glad to have the tree die if it is unwanted.
Do note, however, that not all trees that have been topped die a quick death. In fact, some live on for many years. But with their appearance ruined through topping, the homeowner might actually be better off if the unwanted tree did die. Any gracefulness in form that the tree had had prior to the procedure will be lost forever.
So while "pollarding" and "topping" may appear to beginners to be similar terms, the former boasts a superior pedigree. More thought goes in to pollarding. For example, it is known that only certain types of trees respond well to the practice, so pollarding is limited to those particular types of trees. In contrast with topping, pollarding is first performed when a tree is young. Pollarding is also an ongoing operation, while topping is often done just once, as a stop-gap measure.
When hiring arborists or hiring tree services to trim tree limbs (sometimes referred to as "limbing") that hang threateningly over your home, make sure they have no intentions of topping your tree -- if the tree has any importance to you. Topping, in such circumstances, is a highly disreputable procedure.