This information is provided at the beginning of the story. It may seem somewhat out of place, since it is largely irrelevant to the rest of the story and is never mentioned again. However, this attention to details of the natural world and location-based anecdotes was a significant part of the Romantic period literature, as well as Irving's particular writing style, and may have served to paint a more complete backdrop against which the action was taking place, as well as to introduce foreign audiences to the nuances of the American landscape and folklore.
The particular tree under which the treasure is buried is not given any qualities that make it uniquely suited for the task; it is in the broader consideration of the entire area that its advantages are seen. The inlet (small bay) nearby is said to be an easy place to bring a boat at night directly to the base of the hill upon which the tree grows. The elevation of the hill makes it easy to watch for trespassers, and the trees themselves are distinct and easy to recognize, so that the pirates will know where to look for it when they return.