The word sacrifice means to “make holy.” Man cannot become holy through his own efforts alone. Neither can God make men holy if men will not to their part. Man’s part in becoming holy is to use his agency to obey God. Inasmuch as men obey God, they do not do other things which are evil.
In ancient times the token of man’s obedience to God was the sacrifice of animals. Men killed and burned with fire their best animals to show the Lord that they loved him more than their choicest possessions and to show that they looked forward to the Atonement and death of Jesus Christ.
Since the Savior’s death, the token of man’s sacrifice has been to partake of the emblems representing the Savior’s flesh and blood in what we call “the sacrament.” As men partake of the sacrament, they renew their promises at baptism to become holy in obedience to the Lord. If that token is meaningful, men are making the true sacrifice: a broken heart and a contrite spirit. They are broken-hearted in remembering their offenses against their fellow men and against their God who died for them. They are contrite in a humble determination to offend no more by obeying God in all things. As they obey God in all things, they are cleansed from sin through divine power, and become holy men of God: saints.