Imagine if you had been stood amongst the people as Moses spoke and then demonstrated the covenant by sprinkling or showering you with blood from the sacrifices. We tend to be queasy about blood, ancient people were less so. The blood was significant and significant because it was not just something happening in the distance up at the altar, it was happening to you.
Blood signified cleansing and healing. Blood will have reminded them of an earlier covenant where God in Genesis 9 told Noah that life was in the blood and so it was sacred. To be showered in blood from the altar was to receive life for yourself, to benefit from the animal’s sacrificial death.
Furthermore, it would have been noticeable. If you walked away that day and met people who had not made it to the gathering then they would have been able to tell that you had been there, They would be able to see, smell, feel the blood on you. It should be obvious to those around us that we have been to Jesus and received the new covenant through the shedding and sprinkling of his blood.