Saint Peter referred to Old Testament prophets that were interested in the events of a future Messiah, the Christ. He wrote about "the sufferings of Christ"--which we can with most certainty assume is a reference to the Crucifixion of Jesus, with all its excruciating pain.
But what specifically did Peter mean by "the glories that would follow?
The prophets that spoke of the grace to come to you, searched intently and with the greatest care, trying to find out the time and circumstances to which the Spirit of Christ in them was pointing when He predicted the sufferings of Christ and the glories that would follow. (1 Peter 1:10-11)
The Greek wording is as this: and kai...the tas...(2) after meta...(3) these tauta...(1) glories doxas.
After these would refer to the "sufferings" previously mentioned: "after these sufferings"; then the glories.