Paul wanted the Galatians to realise that his teaching about Hagar and Sarah (Galatians 4:21-31) was the same as the Old Testament prophets, as he quoted this verse from Isaiah 54:1.  The barren and desolate woman was Sarah, the wife of Abraham, who wanted to give her husband a son and heir.  Not being able to have children, she suggested that her husband should sleep with her maid Hagar to get a child.  It was a wrong and faithless decision; Sarah did not trust that God would fulfil His promise as He was far more determined to continue Abraham’s line than she was!
 
However, God, who had promised that Abraham and Sarah would have a child, did keep His promise. Isaac was the first ‘child of promise’ (Romans 9:8) and through him the Old Testament line of faith can be traced all the way to Jesus Christ (Matthew 1:1-16).  Sarah’s joy at the birth of her own son (when she was 90 years old) was overflowing (Genesis 21:1-7). Even though her faith was fragile, God kept His promise when she finally believed His Word (Hebrews 11:11).

Paul sees every believer as a ‘child of promise’ (Romans 4:20-25).  They exhibit the spiritual characteristics of Abraham who trusted God and his faith was counted as righteousness (Genesis 15:6; Hebrews 11:11-12).  Faith, like Abraham’s, often holds onto God’s promise although there is no evidence to do so, except His Word.  Faith in God’s Word is like a healthy plant with deep roots in a barren desert; faith sees hope in failure, finds strength in weakness and takes the next step when utterly exhausted.  Faith trust that God can when we cannot, and dares to stay still while God is at work (Isaiah 40:27-31).
 
We cannot understand how God works, and often He leaves His action until the last moment.  Where we think something is impossible, He performs a miracle.  Even when we interfere with His plan, He still has a way to bring everything together to fulfil His purpose (Romans 8:28).  He is not deterred by our fragile faith but urges us to trust Him even when we think it is laughable.  Trust Him, wait for Him, do not follow your own logic but be content until He reveals His solution.