GEN879 Radak (commentary on this verse) explains that the mark of the brit milah must specifically be made upon the organ of procreation to symbolize that each Jews must overcome his animalistic, physical desires.   This is echoed by Rabbi Judah Halevi, Kuzari 1, 115.   Isaac Irama (commentary of Akedat Yitzchak on Genesis 17) explains the symbolism of the circumcision a bit differently and stresses the national symbol. He says that this commandment binds all Jews together.  By putting a physical demarcation upon each Jews, separating him as a Jew from the non-Jews, all Jews will feel a special kinship, causing more harmony among Jews.   AMEMEI 156-7.