What does Matthew 27:59 mean?

A rich man from the local town of Arimathea, Joseph is a wealthy member of the influential Sanhedrin. This is the religious council which conspired against Jesus (John 11:48–53) and condemned Jesus to die in an illicit nighttime trial (Matthew 26:57–66). Joseph, however, is a secret disciple of Jesus (John 19:38). As with modern legislatures, the Jewish council did not require every member to be present to hold an official vote. Men suspected of being friendly towards Jesus (John 3:1; 7:50–52) were almost certainly not informed of the sham trial until it was over. He has bravely asked Pilate for permission to take Jesus' body away. Pilate has agreed (Matthew 27:57–58).

Joseph wrapped the body in a new (Mark 15:46), clean burial garment. John's gospel tells us that a man named Nicodemus helped Joseph (John 19:39–42). Nicodemus was a Pharisee who had come to Jesus by night to learn more from Him (John 3) and had attempted to influence the Sanhedrin to treat Him fairly (John 7:50–52). Nicodemus brought a large quantity of burial spices, likely at great personal expense. These were typically wrapped against with the body to mask odor and repel insects.

Jewish burial customs did not include embalming or mummification, but bodies were often anointed with perfumed oil in addition to being wrapped. In Jesus' case, a devoted follower had lavished perfume on Him earlier in the week. This, it turned out, was an anointing of His body prior to death (Matthew 26:6–13).