A sacrifice in Biblical terms is referring to an offering made by a person for the atonement of sins, whether it is for their own or for someone else. In ancient Biblical times, sacrifices were first initiated by Adam's sons Cain and Abel, although Abel's sacrifices were accepted by God while Cain's weren't, resulting in Cain being angry enough to kill his brother Abel. By the time of Moses, sacrifices were codified into the Law that God gave to His people Israel, indicating the types of sacrifices and offerings that He considered acceptable. This lasted up until Jesus Christ came in the flesh and offered Himself up on the cross as the sacrifice that would atone for all people's sins for all time, thus abolishing the need for continual sacrifices and offerings that were made once every year by the high priest in the Temple.
In the Left Behind books, sacrifices and offerings were once again put into effect by the Jews in Israel when the Temple was first erected during the early years of the Tribulation, although they were now no longer acceptable unto God because the Temple was erected in rejection to God, according to the two witnesses Eli and Moishe. By the midpoint of the Tribulation, Nicolae Carpathia put an end to sacrifices and offerings in the Temple unless they were made unto him by sacrificing a pig within the Holy of Holies and splashing its blood upon the altar, thus defiling the Temple and making it unfit for use by the Jews for the rest of the Tribulation.
In the Millennial Kingdom, with Jesus erecting a new Temple to replace the defiled Temple that was destroyed by God, sacrifices were once again put into effect, but this time as a memorial for Jesus' one-time-for-all-time sacrifice.