“What does it mean to be baptized for the dead?”
The so-called Latter-day Saints or Mormons practice something they call proxy baptism, literally baptism for the dead. They believe individuals who have not been water baptized cannot enter the kingdom of God — “Even Jesus Christ himself was baptized,” they say — and so, under ecclesiastical supervision, members of their church will baptize a living person on behalf of the unbaptized dead. In doing so, they believe they are putting in place a critical component of God’s salvation requirements for those who can no longer do it for themselves, but would if they could.
The authority they claim for this practice is the apostle Paul and, more importantly in their view, an alleged revelation to the “prophet” Joseph Smith.