The Brit Milah (Hebrew), also Bris (Yiddish) is a ceremony traditionally practiced in Judaism which welcomes baby boys into the covenant. This is a ritual circumcision performed in the presence of family and friends in a ceremonial manner, followed by a celebratory meal. Baby girls were traditionally welcomed with a smaller and more private naming ceremony.
The purpose of the Brit Milah
Jews believe that the commandment to circumcise one's male children was to formalize a covenant between Jews and God. Most Jews claim that circumcision is religiously necessary because of its biblical prescription. According to the Bible, circumcision was enjoined upon the biblical patriarch Abraham and his descendants as "a token of the covenant" concluded with him by God for all generations. The penalty of non-observance was karet, excision from the people (Gen. 17:10-14, 21:4; Lev. 12:3).
Non-Israelites had to undergo circumcision before they could be allowed to partake of the feast of Passover (Ex. 12:48), or marry into a Jewish family (Gen. 34:14-16).
also see: Mohel
According to the Bible, it was "a reproach" for an Israelite to be uncircumcised (Josh. 5:9.) The name arelim (uncircumcised) became an opprobrious term, denoting the Philistines and other non-Israelites (I Sam. 14:6, 31:4; II Sam. i. 20) and used synonymously with tame (unclean) for heathen (Isa. 52:1). The word 'arel' (uncircumcised) is also employed for "unclean" (Lev. xxvi. 41, "their uncircumcised hearts"; compare Jer. ix. 25; Ezek. xliv. 7, 9); it is even applied to the first three years' fruit of a tree, which is forbidden (Lev. xix. 23).
However, the Israelites born in the wilderness after the exodus from Egypt reportedly did not practice circumcision. As recorded in Josh. 5:2-9, "all the people that came out" of Egypt were circumcised, but those "born in the wilderness" were not. Therefore Joshua, before the celebration of the Passover, had them circumcised at Gilgal.
Deut. x. 16 (compare ib. xxx. 6 and Jer. iv. 4) says, "Circumcise the foreskin of your heart," thus giving the rite a spiritual meaning; circumcision as a physical act being enjoined nowhere in the whole book. Jer. ix. 25, 26 says that circumcised and uncircumcised will be punished alike by the Lord; for "all the nations are uncircumcised, and all the house of Israel are uncircumcised in heart."
Evolution of Brit Milah
The original form of circumcision practiced by Jews was more minimal than the form performed today. This rite, milah, initially consisted of cutting off only the tip of the foreskin, the floppy part that extends past the glans in the normal male infant. Two thousand years ago, Jewish hellenists, wanting to assimilate into Greek society, obliterated the sign of their "tip" circumcisions. Most of their foreskins were still intact, so they found ways to lengthen them, to make it look as if they had not been circumcised at all. This practice was unacceptable to the Jewish community at large; the community responded by changing the circumcision rite to remove all of the foreskin. Babies circumcised in this manner could not later hide the fact that they were Jewish.
Control of Sexuality
Some evidence suggests that control of sexuality was one reason for and perhaps the original motivation behind circumcision. The 1st century Jewish philosopher Philo stated that circumcision "represents the excision of the pleasure of sex, which bewitches the mind". The 12th century Jewish scholar Maimonides once argued that the purpose of the Brit milah was to reduce sexual behavior and to weaken the sexual bond between man and woman:
Similarly with regard to circumcision, one of the reasons for it is, in my opinion, the wish to bring about a decrease in sexual intercourse and a weakening of the organ in question, so that this activity be diminished and the organ be in as quiet a state as possible. (...) In fact this commandment has not been prescribed with a view to perfecting what is defective congenitally, but to perfecting what is defective morally. The bodily pain caused to that member is the real purpose of circumcision. None of the activities necessary for the preservation of the individual is harmed thereby, nor is procreation rendered impossible, but violent concupiscence and lust that goes beyond what is needed are diminished. The fact that circumcision weakens the faculty of sexual excitement and sometimes perhaps diminishes the pleasure is indubitable. For if at birth this member has been made to bleed and has had its covering taken away from it, it must indubitably be weakened. The Sages, may their memory be blessed, have explicitly stated: It is hard for a woman with whom an uncircumcised man has had sexual intercourse to separate from him. In my opinion this is the strongest of the reasons for circumcision. 
Similar reasoning can be found in some modern writings, including the Encyclopedia Judaica, which states that circumcision "sanctified the human body and aided in its fight against erotic indulgence".
New ceremonies for welcoming baby girls
In recent years many Jews have developed a parallel ceremony for girls which is now known as the Simchat Bat (Celebration for the daughter) or Brit Bat (loosely, welcoming the new daughter into the covenant.) While still evolving, this ceremony has gained acceptance in Jewish communities of all denominations. Different forms of this ceremony exist in Modern Orthodox Judaism, Conservative Judaism, and Reform Judaism. This newer ceremony is rejected by Ultra-Orthodox Judaism.
The celebration typically consists of a communal welcoming, a naming done over a cup of wine with the quotation of appropriate biblical verses, and traditional blessings. Jews do not perform female circumcision, but the ritual that takes place is considered to have an equivalent meaning. "Moreh Derekh", the Rabbi's manual of the Conservative movement's Rabbinical Assembly, presents a ceremony based on traditional Jewish forms, with a number of options that parents may choose to perform: (A) Lighting seven candles (symbolizing the seven days of creation) and holding the baby towards them, (B) Wrapping the baby in the four corners of a tallit (Jewish prayer shawl), or (C) Lifting the baby and touching her hands to a Torah scroll.