Floors and Ceilings
There are many adventures that have either a floor or a ceiling on them (some have both!). Basically speaking, both are conditions on an adventure: an adventure with a floor cannot occur until a certain number of turns have been spent in the zone, and one with a ceiling will happen as soon as that number of turns have been spent, if it has not occurred earlier. For more detail, see below.
Turn Counters
Before we discuss floors and ceilings, we have to discuss how the game keeps track of the number of turns you've spent and where they've been spent. There are two main counters, and while we don't know their actual names in the database, we will call them turns_spent and turns_in_zone. Turns_spent is the total number of turns spent this ascension, and it's displayed in your character pane.
Turns_in_zone isn't displayed anywhere, but it records the number of turns you have spent in each zone separately (so in effect this counter is an array). However, this counter increments not just with turns spent, but also with combats started. That means that anything that allows you to exit a combat without taking a turn (such as a tattered scrap of paper) will still increment this counter.
Floors
Floors are based off of turns_in_zone. They are set up as conditions on an adventure that compare turns_in_zone to a number (which can be fixed or variable). If turns_in_zone is greater than that number the floor is said to be "expired" and the adventure can occur. Floors can exist on combats, noncombats, and superlikelies. If not the floor is "active" and the adventure cannot occur. The fact that floors use turns_in_zone explains why things such as free run aways and mini-hipster combats count toward the floor, they increment turns_in_zone.
This brings up a good side point, which is that nothing "decrements" a floor, rather they increment turns_in_zone. While the difference is fairly minor, using the former language can obfuscate the way the mechanics actually work.
Ceilings
Ceilings (also called Caps) are also based off of turns_in_zone. There are a couple different types of ceilings. The first works the same way that floors do, it's a condition on an adventure. The difference is that a ceiling checks to see if turns_in_zone is greater than the ceiling, and if it is the adventure is accepted. This type of ceiling only exists on superlikelies.
The second type is new with Pandamonium, and it works exclusively on noncombats. It circumvents the combat-noncombat roll by checking to see if turns_in_zone is greater than the ceiling, and if it is the game proceeds to checking noncombats as though it had rolled a noncombat. This can happen even if you're running combat modifiers to boost a zone's combat rate to 100%.
Other Rejection Conditions
There are a few other types of rejection conditions. The most common is a simple roll, which rejects an adventure if a die roll is not a certain number. This manifests in a few different ways, on superlikelies it's just a condition as a floor would be, but on combats or noncombats it's checked when adding them into the zone list.
The other type checks turns_spent, and if it's below a certain number rejects the adventure. Examples of this behavior are the Strung-Up Quartet and O Cap'm, My Cap'm.