There is a much-loved Ashkenazi custom to hold a "shalom zachar" in honor of the birth of a baby boy. A shalom zachar is an informal gathering which takes place on the Friday night following the birth, usually at home though it may be held in the synagogue or other location. It is customary to serve a variety of refreshments and spirits at this gathering. The shalom zachar custom is actually quite old and even makes an appearance in the Talmud where it is called the "bei shavua haben" or "bei yeshua haben".
The shalom zachar is closely related to the teaching that while a baby is developing in its mother's womb it is taught the entire Torah directly from an angel. Once the baby is born, however, the angel strikes the baby on its mouth which causes the baby to forget everything it had learned. From that moment onwards it becomes a person's lifetime duty to toil in Torah study in order to reclaim this lost knowledge. Furthermore, once the baby has forgotten all the Torah it had learned, the evil inclination "gets to work" making efforts to thwart the child from studying Torah or performing mitzvot. So too, it is taught that one of the reasons that a brit takes place eight days after birth is in order to allow the baby to observe shiva, the traditional seven days of mourning, over all the Torah knowledge that he lost. Based on all this, the shalom zachar has somewhat of a mourning aspect to it. In fact, it is taught that the name "shalom zachar" derives from the word "zachor", to remember, meaning that the shalom zachar serves to remind us of the Torah which was forgotten and now must be re-learned from the beginning.
As a result of the mourning aspect to the shalom zachar it is customary to serve chick peas at the shalom zachar. Chick peas are associated with mourning as round foods symbolizes the circle of life.  Another reason chick peas are served at a shalom zachar is because the Yiddish word for chick peas is "arbis" which recalls God’s promise to Avraham, “I shall multiply (arbe) your seed like the stars of the Heavens.”
It is also explained that the shalom zachar is intended to be an event which welcomes the baby to the first Shabbat of his life. Based on the teaching that all blessings for the coming week have their source in the preceding Shabbat, the shalom zachar is also an opportunity to immerse oneself in the blessings and spiritual benefits which are said to be flowing upon the baby and the family in honor of the brit. Other sources explain that the shalom zachar is an event whose purpose is to give thanks that the baby survived the birthing process.
Additionally, the Midrash compares the brit mila to the offering of a sacrifice. Just as an animal may not be offered as a sacrifice until it has been with its mother for at least a week, so too, a child may not have his brit until he has been under the careful watch of his mother for a week. This is comparable to the idea of a king who refuses to receive visitors until they have first been introduced to the queen. It is taught that the first Shabbat of the baby's life is his introduction to the [Shabbat] queen while the brit which will take place in the coming days is his audience with the King, God Himself.
In some communities the shalom zachar was used as an opportunity for a person to reconcile with his enemies. Indeed the Talmud notes that when a male child enters the world, peace enters the world with him. In order to do this, people would invite their enemies to the shalom zachar in order to receive their blessings at this auspicious time in their lives. The shalom zachar was then seen as a community-wide celebration both in honor of the child as well as the renewed bonds of friendship between former adversaries. In fact, another reason why the shalom zachar is held on a Friday night and not on any other day of the week is because Friday night is convenient for most people to attend such an event. According to this approach, the name "shalom zachar" symbolizes that peace, "shalom", comes with the arrival of a baby boy, "zachar". A mourner who would ordinarily participate in a particular shalom zachar is permitted to do so as his absence would be a public display of mourning on Shabbat which is forbidden.
It is ideal for the shalom zachar to be held in the presence of the baby even if he had not yet been discharged from the hospital. This is reminiscent of the halacha that one is not to console mourners outside of the house of mourning. It is also noted that one of the purposes of the shalom zachar is specifically to "visit the infant". Ultimately, however, the shalom zachar may be held even without the presence of the baby. This frequently occurs when a woman gives birth close to Shabbat and must remain in the hospital over Shabbat along with the baby. In such a situation the father of the baby can hold the shalom zachar at home, as usual.
The shalom zachar gathering is considered to be a seudat mitzva, a meal whose status is a mitzva. Although in our day only snacks and drinks are generally served at a shalom zachar, in ancient times it was customary to serve an entire meal. There was also a custom to visit the mother on the morning following the shalom zachar to partake of refreshments and wish her mazal tov. Even in a situation where it is known that the brit will be delayed for quite some time, the shalom zachar should still be held on the Friday night following the birth, though there does exist a custom to postpone the shalom zachar to the Friday night closest to the brit. When a baby is born on Friday night, some families hold the shalom zachar that same night while others postpone it to the next Friday night, which is the night before the brit will take place. In the event that a baby boy is born in the week on which Yom Kippur falls out on Shabbat, the shalom zachar should be held on Thursday night though there are those who hold it on Friday night, as usual, offering guests the opportunity to recite the blessing upon fragrant flowers and spices since food cannot be served.
It is not customary to hold a similar gathering upon the birth of a girl. Among the explanations for this is that originally the shalom zachar was an event which was associated with the brit more than anything else. In fact, according to some authorities the shalom zachar is essentially an introduction for the brit mila. Indeed, it seems that in ancient times the shalom zachar was not necessarily held on the Friday night following birth as it is today, but rather, it was held the night before the brit was to take place. It might just be that the shalom zachar was moved to Friday night as it is a time when more people are able and likely to attend. As such, it is somewhat irrelevant to the birth of a girl. So too, a woman is not required to learn Torah in the same way that a man is obligated to. As such, there is no mourning for the fact that she has been made to forget her Torah.
According to the explanation, however, that the shalom zachar celebrates the safe arrival of the baby into the world it would follow that a shalom zachar of sorts should be held for a girl, as well. It might just be that the custom of hosting a kiddush shortly after the birth of a girl was intended to serve this purpose. Indeed, many women use the kiddush as an opportunity to publicly recite the hagomel blessing in thanksgiving for a successful childbirth.
Sefardic Jews generally celebrate what is known as the "Brit Yitzchak", which is similar to a shalom zachar, but observed on the night before the brit. This is based on the kabbalistic teaching that the night before the brit is considered to be "spiritually dangerous" for the baby. As such, a quorum is gathered in the house and a special Torah study session takes place, usually consisting of passages from the Zohar. A popular feature of the Brit Yitzchak is to gather children from the community around the baby and have them recite the shema together along with the "hamalach" passage. Many Chassidic Jews also observe some form of the "Brit Yitzchak" ceremony, though they call it the "vach nacht", meaning "the night of watching."
 Terumat Hadeshen 1:269.
 Rema, YD 265:12.
 Bava Kamma 80a.
 Nidda 30b.
 Derisha, YD 264.
 Derisha, YD 264.
 Taz, YD 264:13. See also Brit Avraham cited in Sefer Taamei Haminhagim.
 Migdal Oz, in the Introduction, paragraph 16
 Otzar Habrit p. 89; Zocher Habrit 3:6.
 Bereishit 22:17.
 Teshuvot V'hanhagot 2:202.
 Rabbeinu Channanel, Tosfot, Bava Kamma 80a.
 Taz, YD 264:13; Midrash Rabba, Emor.
 Nidda 31b.
 Orchot Chaim, Mila 9. See also: http://www.chaburas.org/shalomz.html.
 Pri Megadim, M.Z. 444:9; Terumat Hadeshen 269.
 Noheg K'tzon Yosef, Mila.
 Igrot Moshe, YD 3:161.
 Teshuvot V'hanhagot 2:202; Otzar Habrit p. 89.
 Teshuvot V'hanhagot 2:202; For a discussion on this issue see: Hegyonei Haparasha, Tazria p.208.
 Rema, YD 265:12.
 Derisha, OC 305.
 Aruch Hashulchan, YD 265:37. See Tosfot, Moed Katan 28a.
 Pri Megadim, M.Z. 444:9
 See Hegyonei Haparasha, Tazria p.208 for more on this.
 Rivevot V'yovlot 4:233.
 Sefer Chassidut, Shabbat.
 Terumat Hadeshen 1:269; Minhagei Yeshurun 182.
 Dagul M'revava 178.
 Kitzur Otzar Habrit p. 88.
 For more on the absence of a shalom zachar for a girl see: Dagul M'revava, YD 178; Chiddushei Chatam Sofer, Bava Kamma 80a; Torat Ha'adam s.v. Hahotzah.
 Bereishit 48:16.
 Dagul M'revava, YD 178.