"For our sake he was crucified under Pontius Pilate, he suffered death and was buried, and rose again on the third day in accordance with the Scriptures."
As John 3:16 tells us, God gave His only Son for us. This portion of the Creed recognizes what Jesus did for us, that He accepted his fate at the hands of Pontius Pilate to be crucified as those who cheered for Him only a few days before had cheered and greeted Him like a king. He was crucified and as He drew His last breath, He said "tetelesai," meaning, "it is finished" in Hebrew. And then He died. His mother and disciples begged to be allowed to take His body down early so that they could bury Him before the Sabbath. Three days later, they returned to the tomb to find it empty; He had risen.
How do we know He truly died? The Scriptures help to prove this. The testimony that the soldiers pierced Christ's side to prove that He was dead shows that not only "blood but water flowed from His side." The significance of this is that it proves Jesus was not only dead, but had been dead for some time. The blood had started to congeal and separate, which would make it look like blood and water instead of just blood.
"In accordance with the Scriptures..."
Jesus's death was more than just a typical Roman crucifixion. Isaiah, Jeremiah, and other Old Testament prophets had proclaimed long before his birth that Jesus would be born in Bethlehem, a descendant of King David. The prophets foretold more than that, they knew that Jesus would be killed and that He would return three days later to rebuild. The beauty of the Old Testament is how full circle it is with the New Testament, that through the Spirit, it was written what would come to pass.
So we believe, not only that those things happened, but that they happened as the ancient prophets proclaimed to the people of Israel thousands of years before Jesus was born. And it was with His death that He finished what God had started, opening the Gates of Heaven to all of us.