A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
gen 16:1BESTOWMENT OF HAGAR. (Gen. 16:1-16)
Now, Sarai . . . had a handmaid--a female slave--one of those obtained in Egypt.
gen 16:3Sarai . . . gave her to . . . Abram to be his wife--"Wife" is here used to describe an inferior, though not degrading, relation, in countries where polygamy prevails. In the case of these female slaves, who are the personal property of his lady, being purchased before her marriage or given as a special present to her, no one can become the husband's secondary wife without her mistress consent or permission. This usage seems to have prevailed in patriarchal times; and Hagar, Sarai's slave, of whom she had the entire right of disposing, was given by her mistress' spontaneous offer, to be the secondary wife of Abram, in the hope of obtaining the long-looked-for heir. It was a wrong step--indicating a want of simple reliance on God--and Sarai was the first to reap the bitter fruits of her device.
gen 16:5And Sarai said . . . My wrong be upon thee--Bursts of temper, or blows, as the original may bear, took place till at length Hagar, perceiving the hopelessness of maintaining the unequal strife, resolved to escape from what had become to her in reality, as well as in name, a house of bondage.
gen 16:7And the angel of the Lord found her by a fountain--This well, pointed out by tradition, lay on the side of the caravan road, in the midst of Shur, a sandy desert on the west of Arabia-PetrÃ&brvbr;a, to the extent of a hundred fifty miles, between Palestine and Egypt. By taking that direction, she seems to have intended to return to her relatives in that country. Nothing but pride, passion, and sullen obstinacy, could have driven any solitary person to brave the dangers of such an inhospitable wild; and she would have died, had not the timely appearance and words of the angel recalled her to reflection and duty.
gen 16:11Ishmael--Like other Hebrew names, this had a signification, and it is made up of two words--"God hears." The reason is explained.
gen 16:12he will be a wild man--literally, "a wild ass man," expressing how the wildness of Ishmael and his descendants resembles that of the wild ass.
his hand will be against every man--descriptive of the rude, turbulent, and plundering character of the Arabs.
dwell in the presence of all his brethren--dwell, that is, pitch tents; and the meaning is that they maintain their independence in spite of all attempts to extirpate or subdue them.
gen 16:13called the name--common in ancient times to name places from circumstances; and the name given to this well was a grateful recognition of God's gracious appearance in the hour of Hagar's distress.