From Marvin R. Wilson's book, "Our Father Abraham: Jewish Roots of the Christian Faith", page 306:
Other covenants made use of a different kind of visual aid than the blood of an animal. Sometimes the hand was placed under the thigh so as to grasp the genitals (Gen. 24:2,9). Since this vital area was the seat of reproductive power, to touch it in this formal manner might convey the threat that the offending party would become sterile or that his offspring would be destroyed. In any case, the servant Eliezer makes this gesture to Abraham as he is about to leave on a mission that will assure the patriarch of descendants God had promised to him. This graphic act finds its counterpart in a Roman practice that provided the etymological root of our English word "testify". A witness would take the preliminary oath with his hands clutching his own testicles. Such gestures underscore the seriousness of the ancient concept of witnessing. More than reputation was at stake when one pledged his word about a matter. The very existence of one's children -- and even grandchildren -- was potentially in jeopardy.