Answer:
   
   Kosher ("fit") food must meet the complex requirements of Jewish law,
   and the supervising rabbi verifies that such is the case for a given
   food item, or item which will come in contact with food. There are
   restrictions on which foods are permitted during different times of
   the year, and a procedure for slaughtering permissible animals with
   minimal pain to the animal.
   
   The rabbi's role is to decide questions of Jewish law. In the area of
   kashrus, there are hundreds of details that must be met, and thousands
   of "oops, now what?" questions that must be answered. Animals, for
   example, are killed in a very precise manner, by a "shochet", and they
   must be checked internally for disease, have their blood removed by
   salting, feathers removed in cold water, and so on. Kosher wine may
   not come into gentile contact before pasteurization. Vegetables must
   be examined for insects. Because meat and dairy have to be carefully
   separated, precautions against milk-based additives have to taken. The
   complications can be immense.
   
   A rabbi will hire a mashgioch to do the actual supervision. The latter
   is supposed to call in the rabbi when a novel situation comes up.
   
   Note that the Reform movement does not mandate observance of the laws
   of Kashrut. Instead, it advises its members to study the laws of
   Kashrut and to follow those that the individual feels increases the
   sanctity of their life and their relationship to G-d. As a result,
   there are some Reform Jews who do keep kosher. Also, many Jews keep
   some aspect of the kosher laws, such as not eating pork or shellfish.
   
   Rabbis (and others) sometimes recommend avoiding certain food products
   based on concerns other than kashruth, for example:
     * Environmental (e.g. its manufacture harms the environment more
       than necessary)
     * Religious (e.g. a Jewish-owned bakery selling kosher food, but
       open on the Sabbath)
     * 'Tikun olam' [repairing the world] (e.g. the manufacturer complies
       with the Arab boycott of Israel, or mistreats its employees)
       
   Some rabbis choose not to supervise certain products based on
   considerations of the above sort.
   
   For those looking for the traditional point of view, there is a good,
   short primer at [5]http://www.ou.org/kosher/primer.html.