Mark 15:38 says the veil in the temple was ripped from the top to the bottom. What does this mean?

The  tabernacle in the wilderness and the temples that replaced it were filled with symbols which pointed to the coming Messiah and God's plan of salvation.  Paul, referring to the high priests under the Law Covenant wrote, "They serve at a sanctuary that is a copy and shadow of what is in heaven. That is why Moses was warned when he was about to build the tabernacle: 'See to it that you make everything according to the pattern shown you on the mountain.' " (Hebrews 8:5) 

Each temple built to replace the tabernacle (first by Solomon, then Zerubbabel, and lastly Herod) was larger and more ornate than the tabernacle itself and was surrounded by more elaborate structures.  But the sanctuary was built following the pattern of the tabernacle, the two parts being the Holy place [the first room], and the [inner] Most Holy place.  The Most Holy held the sacred Ark of the Testimony in Solomon's temple, as in the tabernacle. This was the place of God's presence. "There, above the cover between the two cherubimthat are over the ark of the Testimony, I will meet with you and give you all my commands…" (Exodus 25:22)  Only the priests were allowed to enter the Holy; and only the high priest was allowed to enter the Most Holy, and this only once a year. The Most Holy was a symbol of heaven itself. 

The temple which existed at the time of Jesus' death was Herod's temple.  Although the Ark of the Testimony was no longer present in Herod's temple, having been captured by Nebuchadnezzar centuries before, the Most Holy continued to be the room where the High Priest sprinkled the blood on the Day of Atonement, to be accepted by God.

The two rooms, the Holy and the Most Holy, were separated by a curtain, also called a veil.  In Herod's temple this veil was approximately sixty feet long and thirty feet wide, and four to five inches thick.  That this massive veil split at the time of Jesus' death demonstrates that it was God's power that tore it and leads us to question why.

The book of Hebrews helps us again.  "When Christ came as high priest…. he entered the Most Holy Place once for all by his own blood, having obtained eternal redemption."  (Hebrews 9:11,12)  Then in Verse 24 we read, "For Christ did not enter a manmade sanctuary that was only a copy of the true one; he entered heaven itself, now to appear for us in God's presence."  Christ's sacrifice was the fulfillment ("antitype") of  the sacrifices required under the Law.

And not only was Justice finally satisfied by Jesus' sacrifice, so that mankind could be raised from death; but "a new and living way" to draw near to God was opened for us.  (Hebrews 10:20)  The night before Jesus died, He prayed, "Father, I want those you have given me to be with me where I am, and to see my glory…" (John 17:24)  When the veil was torn, the way into the Most Holy – heaven – was opened to Jesus' footstep followers.