Why is it that food cooked totally by a non-Jew - without the participation of a Jew - is not kosher?
Food cooked by a non-Jew is generally forbidden to be eaten by a Jew by a rabbinic enactment. The purpose of this law is to discourage excessive socializing with non-Jews, out of concerns that it would eventually lead to intermarriage. (There were also concerns that non-kosher ingredients may eventually make their way in.)
The food may be kosher in so far as it contains no non-kosher ingredients and was cooked in kosher utensils but may not be eaten by a Jew depending on several factors: the nature of the food, the method of cooking, who is doing the cooking and other similar factors.