The altar of repose is a temporary altar where the Communion hosts consecrated on Maundy Thursday during the Mass of the Lord's Supper are placed, or "reserved", for use on the following day, Good Friday.
As Good Friday is the day on which the death of Christ is observed, while the Resurrection of Jesus is observed on Easter Sunday and the anticipatory Easter Vigil on Holy Saturday, Mass may not be celebrated between these days, namely, between Good Friday and the evening Easter Vigil Mass on Holy Saturday which is usually celebrated after sundown. Communion hosts thus cannot be consecrated, and any hosts used on Good Friday or for viaticum for the dying must have been consecrated beforehand.
This structure can be found in Roman Catholic, Old Catholic, Anglican (especially Anglo-Catholic), and some Lutheran churches.