In the tragic relationship of Abraham and Ishmael, we have one of the most significant footnotes in ancient history.  Ishmael is a figure whose extra-Biblical importance far outweighs his minor role as a rejected heir in Genesis.  
    
By Gen 16, the Lord had already spoken to Abram four times about his numerous descendants.  The frequent repetition of this promise is an indication of how concerned Abram was about having no heir.  Sarai had also been wondering about the succession, and she was the one who originated the plan to substitute her maid (slave) as a surrogate mother.

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           She said to Abram, "The Lord has kept me from having children. Go, sleep with my maidservant; perhaps I can build a family through her." Abram agreed to what Sarai said (Gen 16:2).

          

This was an act of desperation and humiliation, an acknowledgment that she had failed in the first duty of a wife -- to   produce a son.  Abraham complied with her plan.  This episode is reminiscent of the fall of Adam and Eve, where the serpent "beguiled" Eve, and she entangled her husband.  In both events, the women were susceptible to follies of creative imagination, while the men were capable of neither responsibility nor headship.  In Abraham's case, his actions flew in the face of God's promise, despite what Paul later wrote in Romans:

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           "He did not waver through unbelief regarding the promise of God" (Rom 4:20).

          

Abraham's lying with Hagar looks a lot like wavering, especially given the repeated promises of God to him. No doubt, he believed he was just helping God out.  Ishmael's conception disrupted Abram's household.  Hagar gained status and power over Sarai.  After all, she was soon to be the mother of Abraham's heir, so why should she continue doing the menial tasks of a servant?  When Sarai realized that her plan had blown up in her  own face, what did she do?  As a typical nagging wife, she blamed Abram, and called on God to judge between them! (Gen 16:5).  There is    unstated irony here: all of this was her own brilliant idea.   But Abram again wimped out.  He ducked the issue and refused to take action or make a decision, he allowed his wife to rule his household.  This was now his second failure in Ishmael's life.

          

Given a free hand, Sarai retaliated harshly against Hagar, causing her to flee to the wilderness.  The Lord sent an angel to meet her.  He told her to return to her mistress, and that she would bear a son named Ishmael (="God hears"), because "the Lord has heard of your misery" (Gen 16:11).  The character of Ishmael is also foretold:  

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            "He will be a wild donkey of a man; his hand will be against everyone and everyone's hand against him, and he will live in hostility toward all his brothers" (Gen 16:12).

          

In the New Testament, Paul speaks disparagingly of Hagar, using her as a symbol of one who bearschildren for slavery and not for inheritance (Gal 4:24-31).  Yet she did no wrong, apart from flaunting her pregancy against her mistress.  She had had no choice in the matter of bearing a child:  it was Sarai's idea in the first place, and she had to submit to Abram.  Then Sarai mistreated her, and Abram refused to protect her! (Gen 16:6)   This was an abused woman.  Yet after running away,  she obeyed the angel and went back to an unhappy home.
             
She gave birth to Ishmael.  Abram evidently felt that God had heard his prayer for a son and heir, and that Ishmael was God's answer.  Also, note that Ishmael was a mixed-race child: half  Mesopotamian, half Egyptian (Gen 16:1 -- Hagar was Egyptian).  Abram was 86 years old when his son was born (Gen 16:16).