First of all, let us consider the significance of the blood. In the Bible, the blood in the life of the flesh. According to Deuteronomy 12:23, "the blood is the life; and thou mayest not eat the life with the flesh." Out of the heart are the "issues of life" (Proverbs 4:23). As such, the blood is that which can pay the price for life--since it is life.
Leviticus 17:11 states, "For the life of the flesh is in the blood: and I have given it to you upon the altar to make an atonement for your souls: for it is the blood that maketh an atonement for the soul." According to the wording of this verse, God gave the blood ("I have given it to you") as the currency by which an atonement could be made for the soul. God chose the blood as the proper payment for life. We can see the significance of the blood, but God made the final call. Life must be purchased with life. That life is the life that is in the blood.
In a similar fashion, whosoever "sheddeth man's blood, by man shall his blood be shed" (Genesis 9:6). Life and blood are interchangeable in this sense. Blood pays for blood. Blood pays for life. Life pays for blood. Blood is the divinely chosen currency for life because life is in the blood.
When we look at the death of Christ on the cross, we find that His blood is a key factor in several aspects of our salvation. Consider the following doctrinal aspects of our salvation and the part played in them by the blood:
REMISSION OF SINS:
Matthew 26:28 - For this is my blood of the new testament, which is shed for many for the remission of sins.
Revelation 1:5 - And from Jesus Christ, who is the faithful witness, and the first begotten of the dead, and the prince of the kings of the earth. Unto him that loved us, and washed us from our sins in his own blood,
REDEMPTION (the purchase of our souls):
Acts 20:28 - Take heed therefore unto yourselves, and to all the flock, over the which the Holy Ghost hath made you overseers, to feed the church of God, which he hath purchased with his own blood.
Ephesians 1:7 - In whom we have redemption through his blood, the forgiveness of sins, according to the riches of his grace; (also Colossians 1:14)
1 Peter 1:18-19 Forasmuch as ye know that ye were not redeemed with corruptible things, as silver and gold, from your vain conversation received by tradition from your fathers; But with the precious blood of Christ, as of a lamb without blemish and without spot:
Revelation 5:9 And they sung a new song, saying, Thou art worthy to take the book, and to open the seals thereof: for thou wast slain, and hast redeemed us to God by thy blood out of every kindred, and tongue, and people, and nation;
Romans 3:25 - Whom God hath set forth to be a propitiation through faith in his blood, to declare his righteousness for the remission of sins that are past, through the forbearance of God;
Romans 5:9 - Much more then, being now justified by his blood, we shall be saved from wrath through him.
Ephesians 2:13 - But now in Christ Jesus ye who sometimes were far off are made nigh by the blood of Christ.
Colossians 1:20 - And, having made peace through the blood of his cross, by him to reconcile all things unto himself; by him, I say, whether they be things in earth, or things in heaven.
Hebrews 9:13-14 For if the blood of bulls and of goats, and the ashes of an heifer sprinkling the unclean, sanctifieth to the purifying of the flesh: How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God?
Hebrews 13:12 - Wherefore Jesus also, that he might sanctify the people with his own blood, suffered without the gate.
ACCESS TO THE FATHER:
Hebrews 10:19 - Having therefore, brethren, boldness to enter into the holiest by the blood of Jesus,
1 John 1:7 - But if we walk in the light, as he is in the light, we have fellowship one with another, and the blood of Jesus Christ his Son cleanseth us from all sin.
Revelation 7:14 - And I said unto him, Sir, thou knowest. And he said to me, These are they which came out of great tribulation, and have washed their robes, and made them white in the blood of the Lamb.
Revelation12:11 - And they overcame him by the blood of the Lamb, and by the word of their testimony; and they loved not their lives unto the death.
I have only given the different scriptures under general topics, but I am sure you can see the importance placed on the blood by the scriptures and the importance of the blood in our own salvation. Without the blood of Jesus, we are certainly lost. But, praise the Lord, that blood has been offered.