Even though the scriptures do not specifically say that Jesus was born in the "stable" we are told that He was placed in a "manger" (which is inside the stable). Since we know that there was no room for them at the inn and they stayed in the "stable" we can safely assume that is the location where Jesus was actually born as well (Luke 2:7). The function of a stable then is the same as a stable today. It is a place where animals were kept. Stables back then were not man-made but natural caves on the surface of the ground which you can see today in Israel. Since they mostly held shepherd's sheep at night they were referred to as "sheep fold caves". This is the type of cave that Mary and Joseph were staying in along with shepherds and their sheep the night that Jesus was born.