The Rema (321) rules that one may only peel onions and garlic immediately prior to the meal. Since the peel is inedible, removing it presents an issue of Borer. Although generally, the good must be removed from the bad, in this case it is permissible to remove the waste prior to the meal, since there is no other way to access the food inside. Peeling under such conditions constitutes "Derech Achila"-the normal way to eat. However, a woman may not peel the onion or garlic on Shabbat morning in preparation for lunch which will take place after one half hour.
Similarly, bananas may only be peeled immediately prior to consumption or the meal. Therefore, a woman may not prepare a fruit salad with bananas early Shabbat morning for lunch. The same is true regarding peeling hard boiled eggs and citrus fruit. However, peeling fruits, such as mangos and apples, in which some of the flesh of the fruit is also removed with the peel, does not constitute Borer, since Ochel (food) is also removed from the Ochel.
The Poskim discuss whether one may peel carrots and cucumbers, as their peel is edible. Some hold that Borer does not apply, and they may be peeled in advance of the meal. Nevertheless, it is preferable to peel them immediately prior to the meal, since, in any event, he is rejecting the edible peel, and therefore it has a status of P’solet (waste).
Hacham Ovadia, in Hazon Ovadia, only permits pulling skin off the chicken during the meal. Even though he is removing the P’solet from the Ochel, it is permitted, since that is "Derech Achila"-there is no other way to access the food.
It is incumbent on whoever prepares the food on Shabbat to be familiar with these Halachot in order to avoid, Chas V’Shalom, the Issur D’oraita (Torah prohibition) of Borer.
