without blemish

But if it has any blemish, if it is lame or blind or has any serious blemish whatever, you shall not sacrifice it to the Lord your God.

Deuteronomy 15:21

This principle of only offering a sacrifice that is without blemish served two purposes for Israel. First, it reminded them of the seriousness of sin. You could not offer imperfections to cover your iniquities. It's what we would want to do but NOT what God requires. Sin could only be atoned by a "perfect" sacrifice. The animal you may have wanted to keep to improve the genetics of your flock was the exact animal meant to atone for your sin at the altar. Sin is a serious offense and atoning for sin required a serious, obedient, sacrificial commitment.

Secondly, this principle taught Israel what real giving was about. It's not the primary lesson. but it is important to realize and follow. God deserves the best of what we have and not the mediocre, the damaged, the second-rate. We should never take the best for ourselves and then offer the leftovers to the Lord. We serve God with the whole of our lives, not the piece-mealed scraps of what little we think we can spare. Worshiping God is not like the penny jar at the convenience store. It is not a small gesture. Giving less than our best to God makes the worship of Him an afterthought, and that is in itself a great sin.