Unfortunately, in tree-care terminology, "girdling" is a word used in two different ways. This means that, unless a context is provided, the reader may not immediately be clear on how the writer is using the term. To help you avoid confusion, a full definition (incorporating both meanings) will be given below.
Girdling as an Intentional Act
One use of the term, according to the United States Department of Agriculture Forest Service, is as follows: "Girdling severs the bark, cambium, and sometimes the sapwood in a ring extending entirely around the trunk of the tree." In this sense, the word usually refers to the intentional killing of a tree.
Many beginners bristle at the very mention of intentionally killing a tree. So some explanation is required. What possible reason could there be to girdle a tree in this way?
Well, let's say that you own (but do not regularly live at) an extensive piece of property that borders upon the forest. On one portion of this property, your plans are to eventually have an open space (perhaps for a lawn area). In the meantime, you need to keep the brush down in this spot as best you can. If a sapling (that is, a young tree) begins to emerge, and you do not have time right away to cut it down, you may want to stop it in its tracks by killing it. So you girdle it. Later, at your leisure, you can remove it. That would be an example of a legitimate reason to kill a tree.
When Girdling Is Accidental
But it can also refer to the strangling of a tree (or shrub) branch or tree trunk by something wrapped around it, which chokes off the flow of nutrients. This is commonly caused by humans (accidentally), by vines, or even by a tree's own roots.
When humans are the culprit, it is often because they have tied a material onto the plant. For example, it may be a wrap used in grafting or a plant label (either the plastic-strip type that wraps around branches or the kind affixed with a string). Leaving such labels on your plant for too long after bringing it home from the nursery or garden center often turns out to be that sort of common landscaping mistake that you kick yourself for later.
Before you know it, the branch will increase enough in girth for girdling to occur. If you need to keep the plant marked with some kind of label, devise your own, instead. The key is to make sure that any label you attach to a tree branch is suspended loosely from the tree, so as to avoid all possibility of future girdling.
Finally, an instance of a tree's own roots girdling it is characterized by Missouri Botanical Garden (MBOT) as a "stem girdling root circles or partially circles the base of a tree at or just below the soil surface."