The term "spiritual sacrifices" occurs once in Scripture, in 1 Peter 2:5. In this passage, Peter is drawing an analogy based upon the religion of ancient Israel, which revolved around a physical temple and physical sacrifices. He shows his readers that they are the building blocks of a spiritual temple, the Church, and they are to offer spiritual sacrifices and not just sacrificial animals.
So what is a "spiritual sacrifice"? Giving a sacrifice involves permanently giving something that has value to the giver, and therefore involves giving up something that most people would rather keep for themselves. A sacrifice is given by a lesser being (man) to a greater being (God) as a form of submission and worship. Animals given for sacrifice in ancient Israel had to be "without blemish," and were some of the finest animals the farmer owned (Exodus 12:5; Leviticus 1:3).
While no scriptural passage defines the term "spiritual sacrifice," there are several passages that describe this kind of sacrifice. In Romans 12:1, Paul wrote, "I beseech you therefore, brethren, by the mercies of God, that you present your bodies a living sacrifice, holy, acceptable to God, which is your reasonable service."
Paul is not saying we literally sacrifice our physical bodies, but that we give our lives to God to use as He sees fit. Many people are willing to "give" God an hour or two a week, but few are willing to completely sacrifice the things they are doing that go contrary to the way of God.
Hebrews 11:4 tells us, "By faith Abel offered to God a more excellent sacrifice than Cain." It seems the sacrifice was "more excellent" because it was a sacrifice given in faith while Cain's seems to have been a sacrifice given out of duty. In that sense, Abel's sacrifice was "spiritual" because it had a spiritual component of a right heart.
Hebrews 13:15-16 says, "Therefore by Him let us continually offer the sacrifice of praise to God, that is, the fruit of our lips, giving thanks to His name. But do not forget to do good and to share, for with such sacrifices God is well pleased." In this passage we see that such things as being thankful to God, doing good and sharing with others are considered sacrifices that please God. The book of Hebrews draws a number of analogies concerning the sacrificial system of ancient Israel and the lessons for Christians today.