“took bread and a skin-bottle of water.” These seem to be very skimpy provisions for Hagar to try to make it to Egypt (but she never got that far, Ishmael grows up in the wilderness of Paran). The skimpy provisions may be to emphasize that Ishmael was to get no inheritance from Abraham.
“skin-bottle.” A “bottle” or container made from animal skin. The Hebrew word only occurs three times and only in this chapter, so although “skin bottle” is a good guess, the actual container might be something different.
[For more on skin-bottles, which were usually made from the skins of goats, see commentary on 1 Samuel 10:3.]
“gave her the child.” According to the custom of the biblical world, the child of a slave born in a master’s house belonged to the master (Exod. 21:4), so Abraham had to give Hagar her son in order for it to be hers in the eyes of the culture.
“wandered in the wilderness.” This could mean “wander” like Abraham did, or it can refer to getting lost. Although there was a road to Egypt, Hagar may still have gotten lost or disoriented somehow.