The speaker is referring to the traditional Christian belief that all the dead will be resurrected on the Day of Judgement. This belief is expressed in "The Service for the Burial of the Dead" in the Book of Common Prayer.
In sure and certain hope of the resurrection to eternal life
through our Lord Jesus Christ, we commend to Almighty
God our brother N., and we commit his body to the ground; *
earth to earth, ashes to ashes, dust to dust. The Lord bless
him and keep him, the Lord make his face to shine upon him
and be gracious to him, the Lord lift up his countenance upon
him and give him peace. Amen.
The speaker in Sonnet 55 is saying that the person he is addressing will remain immortal because his or her essence will be preserved in this sonnet until the Day of Judgement when he or she will return to life in reality, after which that person will have the "eternal life" promised by Jesus in the New Testament and alluded to in the above quotation.
Since this sonnet seems to open in a cemetery with the lines
Not marble, not the gilded monuments
Of princes shall outlive this powerful rhyme...
it would appear likely that it is addressed to someone who has recently died. This sonnet is a sort of requiem or elegy for the person to whom it is addressed. The speaker is boasting that his poetic tribute to the recently deceased friend or lover will outlive all the marble tombstones and gaudy monuments he sees around him.