In this parsha, as in the preceding parsha of Lech Lecha, Sarah is abducted by the ruler of the country, first in Egypt by Pharaoh, and now in Canaan by Avimelech. Although the two episodes differ in certain respects, they both illustrate Avram and Sarah's sound moral judgment as well as providing insight into the social and ethical realities of the ancient Near East.
In Egypt, Avram realized that his wife's beauty was in stark contrast to the unattractive Egyptian women. Assuming that she was his wife, the depraved Egyptians would likely kill him in order to take her. However, by telling them that she was his sister, they would offer him gifts in exchange for her. (In reality, Sarah was actually his niece and at that time a niece was often referred to as a sister. As a brother or uncle, he had the right to accept gifts and marry her off in those days just as a father did.)
Although Avram knew that she would almost certainly be violated against her will, telling them the truth would have resulted in his death and her violation anyway. Therefore he elected to stall for time and drag out the negotiations, hoping for Divine deliverance.
In Parshat Vayera they are faced with essentially the same dilemma. He again refers to Sarah as his sister and again G-d intercedes to prevent her defilement. Avimelech, however, is on a higher moral level than Pharaoh and merits G-d's appearing to him prophetically to reveal Sarah's actual status. Pharaoh, on the other hand, was only prevented from defiling her by the miraculous appearance of a debilitating venereal disease. Since the custom in the ancient Near East dictated that a defiled woman could no longer remain with her husband, Pharaoh sent them away immediately, since people assumed, albeit erroneously, that Pharaoh had defiled her. Pharaoh wanted to make sure that they would not be seen together in Egypt as husband and wife.
Avimelech, however, allowed them to stay in order to dramatically demonstrate that he had not defiled her. Avram himself recognized that Avimelech was morally superior to Pharaoh when he says that his main concern was not Avimelech's immorality but rather, "Surely there is no fear of G-d in this place and they will slay me because of my wife." Avram feared that the degeneracy of Sodom and Gemorrah had spread to Avimelech's subjects as well.
Finally, Avimelech gives Avram a gift of silver and says to Avram, enigmatically, "Let it be for you an eye-covering to all who are with you; and to all you will be vindicated." Avimelech was giving him advice: Use this money to purchase face-covering clothing worn by the undefiled modest women of that time. This will clearly indicate that she has been completely vindicated. Additionally, Avimelech is telling him that in order not to arouse suspicion in the eyes of everyone in the future, he should refrain from calling her his sister so that she will not be in need of miraculous intervention.