The idea of sacrifice is that we give up something for the sake of something else. This is a quality of being selfless. The Bible is very clear that God desires people to be selfless and to make sacrifices to His honour and glory.
Offer right sacrifices, and put your trust in the LORD. (Psalm 4:5)
Offer to God a sacrifice of thanksgiving, and perform your vows to the Most High… (Psalm 50:14)
The sacrifices of God are a broken spirit; a broken and contrite heart, O God, you will not despise. (Psalm 51:17)
With a freewill offering I will sacrifice to you; I will give thanks to your name, O LORD, for it is good. (Psalm 54:6)
I appeal to you therefore, brothers, by the mercies of God, to present your bodies as a living sacrifice, holy and acceptable to God, which is your spiritual worship. (Romans 12:1)
Through him then let us continually offer up a sacrifice of praise to God, that is, the fruit of lips that acknowledge his name. Do not neglect to do good and to share what you have, for such sacrifices are pleasing to God. (Hebrews 13:15-16)
In the Old Testament and specifically under the Law of Moses, animal and grain sacrifices, as well as other types of sacrifices, were required. This was to teach the people about the proper attititude and approach to God. Although the attittude of the offerer was always to be the same, when Jesus came, the method of sacrifice changed, but sacrifice was and still is required.
The Ultimate Sacrifice and Selfless Attitude
God required the shedding of blood to atone for sin. This He accomplished through the willing sacifice of His son, Jesus the Anointed One. Jesus understood his role and willingly offered himself as a sacrifice for sin, leaving us an example to follow.
And walk in love, as Christ loved us and gave himself up for us, a fragrant offering and sacrifice to God. (Ephesians 5:2)
But when Christ appeared as a high priest of the good things that have come, then through the greater and more perfect tent (not made with hands, that is, not of this creation) he entered once for all into the holy places, not by means of the blood of goats and calves but by means of his own blood, thus securing an eternal redemption. For if the sprinkling of defiled persons with the blood of goats and bulls and with the ashes of a heifer sanctifies for the purification of the flesh, how much more will the blood of Christ, who through the eternal Spirit offered himself without blemish to God, purify our conscience from dead works to serve the living God. Therefore he is the mediator of a new covenant, so that those who are called may receive the promised eternal inheritance, since a death has occurred that redeems them from the transgressions committed under the first covenant. (Hebrews 9:11-15)