The NetBible notes say over 200 scenarios for baptism for the dead have been suggested as possibilities! The large number makes sense since there is so little background information on this topic. It’s obscurity leads to wild speculation.
Of those speculations I personally like the one where the person baptized is taking the place of a martyred Christian. Is it possible it’s a baptism in addition to the one when he was baptized for his salvation? Baptism was not exclusive to Christianity and was sometimes used to bring initiates into a specific group. Would it be reasonable to think a Christian might be willing to commit to stand next in line for martyrdom taking the place of a beloved fallen Christian? As we look at the context this is a great fit.
It is also complete conjecture as are practically all the suggestions. Frankly, barring some archaeological discovery, I doubt we will ever know what the reference is.
A list of what it’s not, based on the clear teaching of scripture, is helpful.
It’s not something that saves those:
who don’t choose, wish or want it. Revelation 22:17
without faith. Hebrew 11:6
who do not repent and are not baptized. Acts 2:38
who do bad things while “in the body.” 2 Corinthians 5:10
There’s also room to argue it refers to a practice Paul does not necessarily approve. First, as we have pointed out, this reference to baptism for the dead is obscure. Not only does no other writer mention it in scripture, but neither does Paul mention it elsewhere. If this is an approved practice why is it not described and explained?
Another strong point is Paul does not say “we” but “they” in reference to those who are baptizing for the dead. In doing so he creates grammatical distance between himself and this practice. Was that his intention? One could argue it was not, but it certainly makes his approval doubtful.