In the Old Testament, an animal was brought as a sacrifice for sins.
And according to the Law, one may almost say, all things are cleansed with blood, and without shedding of blood there is no forgiveness.
Today, because Jesus was the perfect sacrifice for our sins, there is no need for animal sacrifices.
Read all of chapter 9 of Hebrews to get the understanding of the New Covenant Sacrifice.
But Christ came as High Priest of the good things to come, with the greater and more perfect tabernacle not made with hands, that is, not of this creation. Not with the blood of goats and calves, but with His own blood He entered the Most Holy Place once for all, having obtained eternal redemption. For if the blood of bulls and goats and the ashes of a heifer, sprinkling the unclean, sanctifies for the purifying of the flesh, how much more shall the blood of Christ, who through the eternal Spirit offered Himself without spot to God, cleanse your conscience from dead works to serve the living God?
When you make a vow to God, do not be late in paying it; for He takes no delight in fools. Pay what you vow!
We as Christians are to be honest in every way. Our word should be enough. We shouldn't need to make an oath, like a promise that we will do what we say. If we feel we have to strengthen our word with an oath, something is wrong with our sincerity. A wise person avoids making rash promises. I have learned not to promise, but to simply say, 'if God be willing'.
Now these sacrifices both in the Old Testament and the New, were no good unless they were brought with an attitude of repentance and a willingness to confess sins.
The reason it is so vital to confess our sins is because a genuine confession shows realisation of sin, holiness, humility before God and a willingness to turn from this sin.
For You do not desire sacrifice, or else I would give it; You do not delight in burnt offering. The sacrifices of God are a broken spirit, A broken and a contrite heart—
These, O God, You will not despise.
Even Jesus' death on the cross will be of little value to us if we don`t repent of our sins and follow Him.
It is like a vaccine for a dangerous disease - it won`t help until it enters the blood stream.
For they indeed for a few days chastened us as seemed best to them, but He for our profit, that we may be partakers of His holiness.
We still need to, as much as we can, make things right with those whom we hurt.
(Resource: Application Study Bible)