Sinning against God requires a blood offering for "forgiveness." Not just any offering though. For those who lived before Christ, they, the Israelites, had to take their first born lamb without spot or blemish, and give it up by faith... showing God that they believed (looking forward) He would send His Son, the Messiah, to cleanse them from sin, as He (God) promised. This was part of the old covenant.

Once Christ came and died, conquered death and hell, and rose again, the payment for sin was made. Now, "all" we have to do, is by faith (looking back) believe that Christ did that for us and accept His payment for our sin. This begins the new covenant, the old covenant having been fulfilled through Christ.