This is my reference: http://stevehanov.ca/blog/index.php?id=130
A vantage-point tree is a way of organizing a set of points so that finding the n-nearest neighbors is as efficient as possible. It builds this tree by picking a point from a set of points (called the vantage point). The median distance from that point to all other points in space is sort of the boundary that splits off that set into two equally sized subsets. This is repeated recursively for each subset that was made until no more points are left (when all points have been made vantage points).
Now searching a VP-tree is where I need help understanding. Basically, when a search is done, a new point is plotted into that space of points, and you need to find the n-nearest neighbors to that point. I especially have a problem with the "tau." and its purpose in this algorithm.