The Blood of Jesus

In order to truly understand why and how the blood of Jesus is sufficient to redeem our sins, we need to first understand three truths.

1. We all have sin.

Romans 3:23 testifies "for all have sinned and fall short of the glory of  God".  In fact, if we claim that we have never sinned, then we are falsely calling God a liar.

If we say that we have  not sinned [refusing to admit acts of sin], we make Him [out to be] a liar [by contradicting Him] and His word is not in us.
- 1 John 1:10 Amplified Bible (AMP)
 

2. Sin separates us from God.

God is holy and he commands us to be holy as well, but with sin we are completely separated from Him.

But your iniquities have separated you from your God;  And your sins have hidden His face from you, So that He will not hear.
- Isaiah 59:2 New King James Version (NKJV)
 

The price (wages) we owe for our sin (debt) is our death.  If we die with our sin, we must still pay this debt of death (the second death).

For the wages of sin is death...
- Romans 6:23 

"That is why I told you that you will die [unforgiven and condemned] in your sins; for if you do not believe that I am the One [I claim to be], you will die in your sins."

- John 8:24 Amplified Bible (AMP)

3. God has decreed that blood makes atonement for sin.

Since we all have sinned, God, being merciful, instituted a way for us to rid ourselves from this sin and its condemnation.  God decreed that  blood would make atonement for the soul (our sins).

For the life  of the flesh is in the blood, and I have given it to you on the altar  to make atonement for your souls; for it is the blood that makes atonement, by reason of the life [which it represents].
- Leviticus 17:11 Amplified Bible AMP

Before Jesus offered Himself on the cross, the Jewish people would sacrifice  unblemished animals as their sinner's substitute.  This act was only  temporary and incomplete.  It would not be sufficient to atone for their sins.

For it is not possible that the blood of bulls and goats could take away sins.
- Hebrews 10:4

Sacrificing a (natural) person would not be sufficient either since all have sinned and that sacrifice could not atone for others sins when that person being sacrificed would already be in debt for their own sin.  Also, the person would not be holy (separated from Satan's spiritual kingdom of which he was born into at birth).

No animal nor person would be sufficient except for one... The only one without sin -  the only one who separated from the kingdom of darkness - the Son of God sent from Heaven to earth being conceived through the Holy Spirit. 

Jesus became the sinner's substitute, dying in our place on the cross, for our sins - fulfilling God's Law on our behalf by His shed blood.

He made Christ who knew no sin to [judicially] be sin on our behalf, so that in Him we would become the righteousness of God [that is, we would be made acceptable to Him and placed in a right relationship with Him by His gracious lovingkindness].
-  2 Corinthians 5:21 Amplified Bible AMP  

Only by the blood of Jesus.

It is only through the shed blood of Jesus that we are redeemed and saved from condemnation.

But if we [really] walk in the Light [that is, live each and every day in conformity with the  precepts of God], as He Himself is in the Light, we have [true, unbroken] fellowship with one another [He with us, and we with Him], and the blood of Jesus His Son cleanses us from all sin [by erasing the stain of sin, keeping us cleansed from sin in all its forms and manifestations].

- 1 John 1:7 Amplified Bible (AMP)

Jesus shed His blood on the cross (an altar) to fulfill God's decreed Law for all of mankind.  Those who receive the Holy Spirit by faith in Jesus, and allow themselves to be led by Him (walking in the Spirit) abide in God's will and will have Jesus' fulfillment of God's Law applied to them (in the spiritual realm) through His blood.

But now [at this very moment] in Christ Jesus you who once were [so very] far away [from God] have been brought near by the blood of Christ.

- Ephesians 2:13 Amplified Bible (AMP)

And having been perfected, He became the author of eternal salvation to all who obey Him.

- Hebrews 5:9 New King James Version (NKJV)

Therefore, since we have now been justified [declared free of the guilt  of sin] by His blood, [how much more certain is it that] we will be saved from the wrath of God through Him.

- Romans 5:9 Amplified Bible (AMP)

There is therefore now no condemnation to those who are in Christ Jesus, who do not walk according to the flesh, but according to the Spirit.

- Romans 8:1 New King James Version (NKJV)