See Semicha article about ordination of rabbis.

Semicha in sacrifices was the placing/leaning [of the hands] usually by a Kohen ("priest") before the offering of a korban ("animal sacrifice") in the Temple in Jerusalem. This involved pressing firmly on the head of the sacrificial animal, thereby symbolically "transmitting" sins onto the animal.

The regulations governing its observance were as follows: The owner of the sacrificial animal was required to lay both his hands with all his might between the horns of the animal just before it was killed. This was to be performed with bare hands. The sacrificer, in case he brought a sin-offering or an offering of atonement, confessed his sins, saying: "I have done thus and so, but have repented; may this sacrifice bring me forgiveness and be an atonement for me." In the case of a thanks-offering or a meal-offering at which sins were not confessed, the sacrificer recited hymns and prayers of thanksgiving during the act.

The symbolism of this custom has been variously explained. According to Philo ("De Victimis") the sacrificer intended his act to imply that "these hands have done no wrong, but have performed good and useful deeds." This, however, applies only to thank-offerings and meal-offerings, and not to sin-offerings or to offerings of atonement. Some rabbinical authorities, followed by some Church Fathers, interpreted "semikah" as meaning that the sacrificer, by laying his hands upon the victim, transferred his sins to it, and imposed upon it the punishment which his conduct had merited (Sforno on Leviticus i. 5; Levi beb Gershon on Leviticus i. 4).

Many scholars hold that these interpretations are not well founded; many hold that there is no evidence that the Israelites believed that sins were actually transferred to the sacrficial animal through the laying on of hands. In this view, the recitation of the liturgical formula, rather than the ritual act, is the determining factor. This explanation of semikah, moreover, does not apply in the case of meal-offerings and thank-offerings, for they had nothing to do with a transference of sins. Since semikah was prescribed for sin-offerings and for offerings of atonement, as well as for meal-offerings and thank-offerings, it must have had a meaning which applied to all these various sacrifices, and must therefore have had some connection with the basal concept of sacrifice. In this view, the hands were laid upon the victim's head as implying on the part of the sacrificer the words: "This is my property, which I dedicate to God."

Now that the Temple in Jerusalem is no longer extant, Jews find atonement for sin in other ways. A classical rabbinic work, Midrash Avot de Rabbi Natan, states:

One time, when Rabban Yochanan ben Zakkai was walking in Jerusalem with Rabbi Yehosua, they arrived at where the Temple in Jerusalem now stood in ruins. "Woe to us" cried Rabbi Yehosua, "for this house where atonement was made for Israel's sins now lies in ruins!" Answered Rabban Yochanan, "We have another, equally important source of atonement, the practice of 'gemilut hasadim' ("acts of loving kindness"), as it is stated 'I desire loving kindness and not sacrifice'".

The Babylonian Talmud teaches that "Rabbi Yochanan and Rabbi Eleazar both explain that as long as the Temple stood, the altar atoned for Israel, but now, one's table atones [when the poor are invited as guests]." (Tractate Berachot, 55a.)

The traditional liturgy of the High Holidays (Rosh Hashanah and Yom Kippur) states that prayer, repentance and tzedakah ("charitable actions") are how one atones for sin.