"Planescape" is a paper and pencil rpg Dungeons and Dragons campaign setting, or rather, a collection of most realms besides the cooporeal which is other campaign settings "Grayhawk" and "Forgotten Realms", and the demiplace of Dread, which is the gothic horror setting, "Ravenloft". "Planescape" is all the other realms (Acheron, Mechanus, elemental planes, mount celestia and the many layers of hell, astral plane, etherial etc) all connected in the campaign setting key location, Sigil. Sigil is a vast city constructed on the inside contours of a giant ring, floating through ther cosmos. It's governed by a mask-wearing god figure, the Lady of Pain and operates as a starting point of many Planescape adventures due to the numerous doorways to the other realms that can be found in the vast city, if you only know where to look.
The premise of the "Planescape" setting, is that rpg characters eventually grow too strong for their native realms, coming across abilities and/or othe various ways to move on different planes of the vast Multiverse. Thus the campaigns based on Sigil and thereafter, are usually of the high-level power-playing type, where characters assume the roles of hardened interplanar cosmonauts, fighting dreaded Baatezu in the pits of hell or getting lost in the labyrinthine machinery of Law realm Mechanus.
Planescape: Torment is a computer game based on said campaign setting, created by - I think - Black Isle, more popularily known for the Baldur's Gate series. The Baldur's Gate series are based on the "Forgotten Realms" campaign setting, which has proven to be the most enduring - both in popularity and in added material - item in the TSR (and now Wizards of the Coast) catalogue. I haven't played Torment, but it's said that it is a very good RPG, with a great story, nice gameplay depth and vivid recreations of the various realms. As I didn't care much for Baldur's Gate, I am a bit sceptical about all this, but then again my preffered DnD computer games remain the three Eye of the Beholder games and the original gold-box Pools of Darkness so maybe I'm not the one to ask.
Hope my geekness has helped.