It's an infinite family of metrics - you provide an n (a positive integer) and get back a metric.

So if you pick n=1 you get d(x, y) = |x| + |y|, which is the taxicab metric. You can apply this metric to a Euclidean space of whatever dimension you like, just substituting the appropriate definition of |x| and |y|. For 1-dimensional space you would use |x| = abs(x[0]), for 2-dimensional space you would use |x| = sqrt(x[0]**2 + x[1]**2), etcetera. Hope that helps.