In Judaism, we understand the act of ritual circumcision to be a physicalized representation of accepting the covenant of Abraham. It is a way to carry the covenant not only bound into one's flesh, but into the flesh we use for procreation, symbolic of our commitment to passing the covenant on to our children.
This act does not make us holier, but rather marks us out as unique, inheritors of Abraham's covenant, members of the Jewish People. It is part of how we define who we are, as dedicated Jewish men, bound in every part of our lives to God's service.
If a Jewish man is not circumcised, he is spiritually cut off from the Jewish People, and he is rendered incapable, under Jewish Law, of participation in Jewish ritual life.
There is no one accepted answer for why women have no equivalent physical ritual. Some say that it is simply a matter of their genitals being mostly internal. Others say that it is because in ancient times, men customarily took oaths holding their genitals (hence the Latin derivation for the term "testimony"), while women did not, and so no equivalent was deemed necessary. Others say that women's role in the covenant is marked by childbearing, as we count Jewish identity matrilinearly. Still others say that women have no need of a physicalized reminder because they are more adept at grasping spiritual commitments. There are many, many other opinions also. And of course many modern scholars simply feel that there is no equivalent ritual because ancient society was androcentric, and simply did not think to be inclusive of women in that way.