In a series of rabbinical ordinances instituted as a safeguard against intermarriage and assimilation, the Sages forbade the consumption of the wine, bread and cooked foods of a non-Jew, also when these do not contain any non-kosher ingredients.
The prohibition of food cooked by a non-Jew only applies in the following cases: a) it is a food that cannot be eaten raw; b) it is an important food, "fit to be served at a king's table."
The prohibition of non-Jewish bread applies to home-baked bread, not to bread prepared in a commercial bakery. Nevertheless, it is the custom of many communities to use only pas yisroel ("Jewish bread") rather than avail oneself of this leniency.
If a Jew is involved in any part of the baking or cooking process (e.g, he turns on the oven), the baked or cooked food is permitted. Sephardic tradition requires the food to actually be placed on the fire by a Jew.