Time is an important concept of everyday life and a powerful tool in the hands of the Dungeon Master. However, it is a difficult thing to get right. The amount of time to accomplish tasks as well as the actions that the world takes as time passes are extremely important elements that I wish to discuss. This will also partially intersect with my previous article about the world, but there are quite a few things I wasn't able to discuss in that article because of the scope. The main goal will be to inspire thinking on this topic and how it can be used to make unique and exciting campaigns and situations.
The resources available to the party are dependent on the amount of time the party members can spear to gain resources. It may be as small as taking a short rest in D&D 5th edition or as large as going on a multiple year long journey to obtain magic sword number 5 in order to be able to challenge the big bad (alright, that is a bit cliche but still). However, doing so will naturally affect the difficulty for the party to accomplish their task. If the party can rest after tackling a room with no penalty, it may prove too easy if the dungeon was designed to be tackled all at once (it would be just fine if the intent was to go extremely slowly and one room at a time).
There are a few ways that time could play a role. If the players wait around in the dungeon, maybe some monsters will stumble upon them (our good old friend the wandering monster table provides) and prevent their rest. The passage of time has an effect on the world in this case. However, there may be cases where this doesn't make sense such as unintelligent undead not wandering past the rooms they were instructor to stand and guard (giving the players access to more rest). Time could still be an important factor because of external factors such as deadlines or competitors (bad guys could be getting stronger while the players sleep). There could also be cases where you reward caution or simply use the passage of time to bring the world to life (looters get into the dungeon while the players are resting in their camp, clear a couple rooms but then die).
Players will end up losing time when confronted by an enemy army (army battles take time), an overfull river or a thick slab of stone. It's only natural for obstacles to take time away from the players as they overcome them. In such cases it becomes necessary to consider what could happen in that amount of time that the players are occupied. It could be nothing but the consideration needs to be made.
Take for example the situation where after going through a portion of the dungeon, the players hit a solid wall of stone. Picking their way through will take time, if they have the tools and possibly tire them out (you might not have them roll for fatigue after just one such stone wall). If they don't have the right tools to do so, it will take even more time for them to go back to a town and buy supplies (this may not necessarily be the case if it was a passage filled in with rubble instead).
Bring the World to Life
The passage of time can be used as a central point of a campaign (for players who have very long lifetimes and are combating other beings with lifetimes just as long) but it can also be used in order to make the world feel alive. It is very easy to get into a situation in a tabletop role-playing game where the only actions take place in a small radius around the party (this may be even desirable for some grounds). However, it is just as valid to have the entire world moving along as the players work.
Let's use the situation of a big battle as a case study. Right after the battle takes place it will leave an area filled with bodies and equipment. Stories may be told back in the cities the players visit. If the players pass by the same area a few days later and see large grounds of scavengers (grave robbers and carrion eaters alike), it starts to make the world seem like it actually functions. They may come across the same area months later and see necromancers using it as a source of materials for their work, now that the area has become safer. All of this starts to create a story for this tiny area and makes the event all the more meaningful to the players (especially if they are responsible).
The concept of time is a generally interesting concept and it remains so in tabletop role-playing games. It allows the creation of many situations and the exploration of many ideas while in play. I cannot hope to cover every idea or way to do so, but I hope that at the very least this serves as a starting point and inspiration. As always, feel free to comment.