I have heard and read many tracts devoted to the legitimatization of the practice of praying for the dead but none have gone into detail of what exactly that term means. Is it praying for a shortened time in purgatory? Is it prayers that God may be merciful on the departed soul, etc? What is meant by that (pragmatically speaking)!?
Yes, purgatory but also your prayers now can help them get into heaven. Even though they are already in heaven(purgatory) or hell God lives outside of time so he see’s your prayer at the time right before their death even though you may be praying them years later. Kind of an ausome concept when you sit down and try and think about it.
We pray for the dead to remit the temporal punishment of their sins.
The Catholic practice of praying for the dead is rooted in the Catholic beliefs in Purgatory, the double consequence of sin (both eternal and temporal punishment), and the Communion of Saints.
To understand praying for the dead, you must understand these other three Catholic beliefs.
The relevant sections in the CCC are #1030-1032 and #1471-1479.
The Catholic Encyclopedia has an article that discusses the Biblical and historical support for the Catholic practice of prayers for the dead:
Speaking of satisfaction in the rigorous sense, the living can offer to God, and by impetration move Him graciously to accept, the satisfactory value of their own good works on behalf of the souls in purgatory, or in view of it to remit some part of their discipline; in this sense we may be said to satisfy for the dead.
But we do not and cannot know the exact degree in which benefits actually accrue to them, collectively or individually. The distribution of the fruits of the communion of saints among the dead, as among the living, rests ultimately in the hands of God, and is one of the secrets of His economy.