What is an index fossil? How is it used to identify the relative age of rocks?

Index , as used to precisely date short geological time intervals, are the skeletal remains of such species of plants or animals that combine the following two characteristics: a geographically extended habitat, and a short existence.
If I were to date the 20th century in brief, identifiable time frames of, say, 10 or 20 years, my choice for index fossils would be movie . Veronica Lake for the ‘40s, Marilyn Monroe for the ‘50s, James Dean for the ‘60s etc.
Why? Because you can find their films (fossils) everywhere and, when you got one, you know exactly in what time period that film was made. Granted, I could not use John Wayne or Charlie Chaplin whose long careers spun a longer interval than the bracket I have indicated. But Brigitte Bardot would be fine (’55-’65), and so would be Rodolfo Valentino (1915-25).
Most geological dating is done by identifying fossils as they are found incrusted in a rock series.
Supposing you ran into an unknown fossil on the island of Java and, by other means, you could place it accurately in the stratigraphic time scale. What good would your discovery be to your colleagues if they could not repeat your finding anywhere else outside of that island? Hence, for generality, the necessity of the broad habitat.
Suppose now that you found a fossil at the base of a long geological series that you might be sampling on the rock-face of a mountain. Suppose also that, as you climbed up with your hammer from the Triassic to the Paleocene (an interval of a couple of hundred million years), you kept finding the same fossil everywhere though in different epochs and terrain.
Of what use would that relic be to you for dating purposes? How discriminating would his presence be to tell one age from another?
Index fossils tend to be benthonic remains. But index microfossils are usually pelagic. The maritime evolutionary cycles are shorter than the subaerial ones and organisms can move and migrate with greater ease transported by oceanic currents. Foraminifera are regularly used by micro paleontologists for dating purposes. Their life span is of the order of a few thousand years and, as for geo-graphical distribution within a given time frame, they can be found everywhere?
Let’s close this answer with the exercise proposed by the Cloudfront.net site with the above image:
1) Would you say that the trilobite found at the base of the series (A) in all four location is an index fossil? 2) Would you say that the triangular brachiopod to be found in (A, B and C) of all four location is an index fossil? 3) Would you say that the seashell (probably an ammonite), present in all C location is an index fossil?4) Would you say that the horizontal gastropod (Turritella?) found anywhere, every time, is an index fossil?
One more clue, only two of the above are index fossils, and they are in A and C.
Have fun with geology.