The word sacrifice means different things to different people. Some people think that sacrifice means the act of making an offering to a god such as when the ancient Hebrews killed animals on the altars to atone for their sins. Other people think it means to give up one thing for another. Others consider it to be the act of destroying or surrendering something valued or desired to satisfy a higher need. I like the following description of sacrifice: Giving up something good for something better.
The Lord requires us to be willing to sacrifice our earthly possessions, time and energy to further His work and defend His kingdom. He commanded, "Seek ye first the kingdom of God, and his righteousness" (Matthew 6:33). People have always been tried and tested to determine if they would put the things of God first in their lives. The willingness to sacrifice shows our obedience to God.
The law of sacrifice has been practiced since Adam and Eve built an altar and offered sacrifices to God. Heavenly Father commanded His people to offer as sacrifice the firstlings of their flocks - perfect and without blemish. The ordinance of sacrifice was a reminder to God's people that the Firstborn of the Father would come into the world, live a perfect life, and offer Himself as a sacrifice for our sins. (See Moses 5:5-8).
Jesus Christ came into the world just as the prophets had taught. Through His atoning sacrifice, He made it possible for everyone to be saved from physical death through the Resurrection and to be saved from their sins through faith in Jesus Christ. The atoning sacrifice of Jesus Christ brought to an end the shedding of blood for sacrifices. The outward sacrifice of blood was replaced by the ordinance of the sacrament as a reminder of the Savior's great sacrifice. We should partake of the bread and water of the sacrament often as these emblems remind us of the Savior's body and of His blood, which He shed for us.
Even though we no longer sacrifice by the shedding of blood, we are still commanded to offer sacrifices. Through latter-day revelation, the Lord said: "Ye shall offer up unto me no more the shedding of blood, … and your burnt offerings shall be done away. … And ye shall offer for a sacrifice unto me a broken heart and a contrite spirit" (3 Nephi 9:19-20). A person who has a "broken heart and a contrite spirit" humbly offers to the Lord a deep sorrow for sins in repentance of them.
We can have a broken heart and a contrite spirit when we humble ourselves and become willing to receive the will of God and the counsel of His leaders here upon the earth. Having a broken heart and a contrite spirit also means to feel a deep sorrow for our sins and to have a sincere desire to repent and become clean again.
Lehi, a prophet in the Book of Mormon, emphasized the importance of offering this sacrifice: "Behold, [Christ] offereth himself a sacrifice for sin, to answer the ends of the law, unto all those who have a broken heart and a contrite spirit; and unto none else can the ends of the law be answered" (2 Nephi 2:7). In other words, if we don't offer a broken heart and a contrite spirit, we have no claim on the blessings of the Atonement.
Sacrifices take many different forms. A "living sacrifice" is made when we are willing to give everything we have to build the kingdom of God on earth and to labor to bring forth Zion. (See 1 Nephi 13:37.) Our daily activities can be a sacrifice as we strive to put the things of God first.
I know that it is difficult to give up something I value a lot, but I find it much easier when I remember that I am only trading what I have for something better. I know that sacrifice brings many blessings with the end result becoming worthy to live in the presence of God and to live eternally with Him and our loved ones. As we humbly offer our sacrifices, we strengthen our testimonies of the gospel. Sacrifice is not easy but it brings something better than what we give up.