Ironman
Rules
When playing Ironman style characters can not use any items they do not find themselves, repeat/replay areas, or buy items from NPCs. Ironman characters are generally hardcore, and are forbidden to return to town or interact with NPCs in any way other than as required to complete progress-stopping quests. There is naturally no twinking or muling or other such activities either.
Common Uses
Ironman is often played in parties, where several friends begin at the same time, all with brand new characters, and see how far they can make it through the dungeons without dying, running out of equipment, etc.
Background
This style of play enjoyed some popularity in Diablo I, where 3 players worked together cooperatively, each playing a different class. Items were traded freely between the party, with the Rogue getting the best ranged items (bows only then), the Sorcerer the spellbooks and mana pots, the Warrior the melee weapons and armor so he could tank, etc.
Cooperative Ironman play can be extremely powerful in Diablo II, thanks to the complimentary skills and shared spell effects.
Example
A group of 8 players from Germany completed the entire game, including the Pandemonium Event, with naked, hardcore, LotL, Ironman characters, who additionally forbade the use of the most powerful minion summoning skills.
Their character lists, techniques, and videos of the achievement can be seen here.