Genesis 20:16-18 meaning

Abimelech tells Sarah, "I have given your brother a thousand pieces of silver." Notice that Abimelech calls Abraham Sarah's brother and not her husband. A thousand pieces of silver was a large amount at that time (Genesis 23:15-16, 33:1, 37:28). 

The word vindication means a covering of the eyes. It was to cover the offense and exonerate Sarah. The covering was provided by a payment for an offense against someone in order to make amends. Metaphorically, people's eyes were covered so they could not see Sarah's shame. By making this payment Abimelech was showing everyone that he intended no harm or wrong towards Sarah and Abraham and that his actions were well-meaning. In other words, the king was settling his debt with Abraham and Sarah. 

Since his offering was in good faith, no one should have a reason to criticize or discredit Sarah. In this way, she was exonerated or pardoned in the sight of others and the wrong had been made right. Her honor had been restored showing there was no sexual misconduct on her part. 

Abraham prayed to God to heal Abimelech and his household. The Hebrew word "palal" is the most common word used to describe the general act of prayer. It means to intercede or mediate for another (Numbers 11:2, 21:7; Deuteronomy 9:20, 26; 1 Samuel 7:5; 1 Kings 13:6; Ezra 10:1; Daniel 9:4, 20). 

Abraham prays for Abimelech, and God healed Abimelech and his wife and his maids, so that they bore children (verse 18). God, not Abraham, is the healer. These women had their fertility restored, so that they bore children. Numerous children were considered a great blessing (Genesis 17:20, 22:12, 26:24, 28:3; 1 Samuel 2:20).
The Lord had closed fast all the wombs of the household of Abimelech because Abimelech had taken Sarah. A fruitful womb was considered a divine blessing (Deuteronomy 30:9). This may be the manifestation of the penalty spoken of by God as "death" by a barren household (vv. 3,7). Through barrenness, their tribe and inheritance would die. The next chapter describes how God opened Sarah's womb so that she may conceive and give birth to the promised child in her old age.