In God's kingdom, blood is an important commodity. We can see this in the New Testament where the blood of Jesus is frequently referred to. In fact, at the Jerusalem Council (Acts 15), of the four Levitical laws Gentiles were required to keep, two were about blood: "abstain from...the meat of strangled animals [if strangled, the animal's blood would stay in the meat] and from blood." (vs. 20)
Blood is a spiritual cleansing agent. Revelation 7:14 says that the survivors of the Great Tribulation will have their clothes "made white in the blood of the Lamb"; Hebrews 9:14 talks about how the blood of Christ cleanses our consciences and Hebrews 9:22 asserts that nearly everything needs to "be cleansed with blood" and that there is no forgiveness without blood.
This helps to explain why, after he had read the Book of the Covenant to God's people at the foot of Mt. Sinai and after the people responded affirmatively that they would do all that the Lord told them, Moses took bowls of blood and "sprinkled it on the people."
Picture this in your mind! The people had all prepared for this day of encounter with God. They had bathed and dressed in their best clothes (Exodus 19:10, 11) and now they were getting blood on their clothes and this was a good thing? Remember how bloodstains are so hard to get out of our clothes? Back then, they didn't have the chemicals we have to help them do so. From this day forward, the clothes they wore on the day they faced God, their best clothes, would be bloodstained--another reminder of their covenant to God and their uniqueness amongst the nations.
We too have been sprinkled with blood--the blood of Jesus Christ. Is it as visible as the blood of bulls sprinkled on the people back then?