The plot setting (or flag) makes objects resist attempts by a player to be rid of them. This is nominally to ensure that a module's story (the plot in the literary sense) can be played out, but it also has other uses (such as protecting key support characters from a player's foolishness).
Plot creatures tend to be named non-player characters whose removal from the story would be detrimental to the player, especially when that creature is required to advance the story. They cannot be harmed in any way. Hostile actions taken against a plot creature tend to be ignored by the AI (although an occasional bug may lead to "non-hostile" plot characters attacking a player character).
Placeables and doors that have been flagged as "plot" cannot be damaged. Any attempt to bash them will first go against their hardness, resulting in the usual message about damage being resisted, but any damage that is not resisted will simply be ignored with no additional feedback to the player. Symptoms of attacking a plot placeable or door include an unusually regular amount of damage resisted with each attack while the target remains undamaged. (A more reliable test is to use a weapon with a non-physical damage bonus, as that would ignore hardness.) Plot objects are also immune to the knock spell, so neither might nor magic can get a character past a locked plot door or into a locked plot chest. Some, but not all, locked plot objects are also immune to the open lock skill, requiring a specific key or mechanism to be opened.
The use of the plot flag on items necessarily has a different consequence, as no items can be damaged. Essentially, the plot flag is an unsellable flag for items; a plot item cannot be sold, and no other special restrictions apply unless specifically implemented by a module. In particular, a plot item can be dropped (on the ground or into a chest), so the plot flag does not ensure that a player keeps a plot-critical item, only that the item does not end up in a store. Ironically, the best setting for some plot-critical items is not "plot" but "cursed" (as was done for the relic of the reaper in the Hordes of the Underdark campaign).