Why don’t we eat after shkiah on Shabbos afternoon unless we wash?
The idea is that after shkiya, it is a little before the time to daven to make havdalah. Before making havdalah we are not allowed to eat or drink anything (except water), therefore we don’t eat or drink after shkiya. The halacha though is that if we are in middle of a bread meal, even though the time to make havdalah has arrived, we don’t have to stop the meal. Therefore, if we wash and eat a bread, we may continue to do so.
It should be noted that if one is person is hungry or thirsty, it is possible to still eat until half an hour after the time when you can daven maariv. (In Eretz Yisroel it is not applicable because many daven maariv less than half an hour after shkiya).
O:CH 299-1, M:B 299-1, Aruch Hashulchan 299-1.