What does Genesis 16:1 mean?
In the previous chapter, the Lord had directly promised Abram that his heir would be his own flesh and blood (Genesis 15:4). Abram would have a son, and not merely a servant, as his heir. That specific promise does not seem to have been given to Sarai, Abram's wife. At the very least, she does not seem to trust God's work in the situation. It's also possible she doubted that Abram's heir was meant to be born through her. In any case, it had not happened yet, and the ticking of the clock must have sounded quite loud as Abram was now well into his 80s and she in her 70s.Sarai has an idea to help the plot along, however. Hagar was Sarai's servant, or "slave girl." Slavery in this era was vastly different from what modern people picture. A closer term for today's world might be an "indentured servant." This was a one-sided arrangement, to be sure, but the relationship, as seen in the following verses, was not as simplistic as slave-to-master. It's possible that Sarai took possession of Hagar, an Egyptian, when Sarai had been taken by the Pharaoh for his wife (Genesis 12:10–20).
Sarai proposes her alternative plan to provide Abram an heir in the following verse.