“So the servant placed his hand under the thigh of Abraham his master, and swore to him concerning this matter.”  Gen. 24:9

The phrase “place your hand under my thigh” is awkward to speak, and is most likely referring to the male organ or testicles.  Today we take oaths on a sacred object, such as a bible.  Jews may swear on a t’fillin or a Torah scroll (Plaut).

According to Rashi, the fact that God asked Abraham to circumcise himself, or perhaps the importance of the seed of Abraham and the promises it held for the future, made the organ the most significant object to place hands on.

Conversely, for the servant, an oath taken in such a manner may mean the curse of sterility if the oath is not kept. (Plaut)