Bishul Yisrael (בישול ישראל)
Certain cooked foods that a Jew must have a hand in cooking. A stricter standard some people look for.
The Sages asked that some foods cooked by a non-Jew have Jewish involvement in the cooking. It only applies to foods that are (1) not normally eaten raw and (2) 'important' enough to be served at a respectable meal. Foods eaten raw, or considered minor, are not included.
Cooking done by non-Jewish staff in a factory or restaurant.
For Ashkenazim it's generally enough that a Jew lit the flame; for Sephardim a Jew usually needs to place the food on the fire or do the actual cooking. Why: The Rema (Ashkenazi practice) holds that a Jew lighting the flame makes it 'a Jew's cooking'; the Sephardi practice requires more direct involvement. This is why kosher supervisors light or cook on site.
Foods that are commonly eaten raw (like many fruits and vegetables) cooked by a non-Jew.
Not included in this standard — they're fine. Why: The rule only covers foods not normally eaten raw. Anything people happily eat raw is excluded from the start.