Translation
But He said this as a sign [indicating] by what sort of death he will glorify THEOS. And having said this, He says to him, “Follow me.”
Paraphrase
But when Jesus said this it was a means by which He indicated that Peter would glorify THE CREATOR AND OWNER OF ALL THINGS by being crucified. After Jesus made the previous statement, He said to Peter, “follow me.”
Peter's Story
Peter was disappointed. He had wanted to see Jesus return in great power. He remembered Jesus saying on two occasions (Mt 16:18 & Mt 24:34) that His powerful and glorious return would happen during their lifetimes, or that of an average person in their generation. Now Jesus was indicating that Peter would not see it, rather he would grow old and helpless, and He may have been implying more than that, Peter was not sure. John was able to write about it after Peter’s death and so he knew that, yes, Jesus had intended to convey a secondary meaning in His statement.
We know from church history that, when it came time for Peter to be martyred, and when he found out it would be through crucifixion, he did not want to be crucified the normal way because he did not feel worthy of dying as Jesus had died. So he asked to be crucified upside down. Amazingly, his executioners agreed to his request. This would involve a different kind of death, one in which too much blood goes to the brain for too long and blood vessels begin to rupture. But the point Jesus was making still held true. Peter’s arms were indeed stretched out and he did die from being crucified, albeit upside down.