Time

In addition to standard units of real-world time (days, hours, minutes, etc.), V23 measures time in a number of ways that doesn't have anything to do with clocks or calendars. Some of these units are primarily used to talk about the structure of the game, some are helpful for pacing or building dramatic tensions, and others are simply a way to discreetly subdivide game events for the sake of gameplay. These are described below, from (roughly) longest to shortest.

Campaign

Traditionally, the term campaign refers to the entirety of a particular game, usually centered around a specific group of characters. The exact players and characters in the group may change over time, but there's usually some sense of continuity from one adventure to the next. If you think of your game as a TV series, a campaign consists of all the individual seasons taken as a whole. Some campaigns have a larger story that runs through the entire series, but it's just as common for the campaign to simply be the ongoing chronicle of the PC group's adventures.

Story Arc

If your campaign is the entirety of a series, a story arc is a season, consisting of a number of individual adventures (episodes) that build upon one another to tell a larger story. Since the conclusion of a story arc should change the status quo in some meaningful way (whether for the PCs or the world at large), starting a new story arc often means changing the premise of the game, expanding its scope or power level, and making changes to PC party's role or membership. It can be a bit like starting a new game, but in this case you've got some established history to build upon.

Subplot

A subplot is just a secondary story arc that runs alongside and occasionally intersects with the campaign's main plotline. Examples include character arcs, ongoing interpersonal conflicts or drama between members of the PC group, b-stories, side quests, and player-initiated schemes. Subplots can resolve over the course of a single adventure or weave through the entire campaign as needed and do not need to coincide with events of the main storyline. In come cases (especially for storylines that don't involve the whole party), a significant portion of a subplot may take place off-screen during downtime, with the relevant players only role-playing the most exciting or interesting plot points.
In addition to the subplots that involve the PC group, the GM can refer to subplots that don't involve the characters directly to create a more dynamic game world. This kind of background flavor also allows the GM to introduce plot-related information with a bit more subtlety than is possible when everything is a plot point.

Adventure

An adventure is like an episode of a TV show or an issue of a comic book, consisting of a single story, mission, or subplot that may or may not be related to the larger ongoing story. Adventures are often designed to play out during a single game session, but just like some TV episodes are "To Be Continued..." some adventures may take multiple game sessions to tie up. The amount of game time that passes during an adventure varies considerably depending on the plot. Some cover only a few hours of time in the game world, others may include long stretches of travel or other game time that result in weeks or months of game time passing between the beginning and end of the adventure.
Despite the extreme variations in the amount of game time that can pass during an adventure, some character abilities and other game events have a per-adventure limit. For example, a character may be allowed to call upon a an ally once per adventure. While it's certainly nice when such limits have a logical explanation within the game world (your ally has stuff to do and will stop agreeing to help you if you constantly ask for favors), in reality these sorts of limitations have more to do with gameplay and drama than story logic. Allowing characters to use powerful abilities at will makes the game less challenging, less interesting, and more predictable while also sucking everything cool or special from the abilities themselves through sheer repetition. Forcing players to choose when it's time to pull out the big guns, on the other hand, adds drama to the game. If you've ever watched wrestling, it might help to think of per-adventure abilities like a wrestler's finishing move: There's nothing stopping the Hulkster from doing only leg drops the whole match, but it would make the match really boring and completely take the excitement out of the final match-ending move--in part because there'd be no way for the audience to know that the latest in a series of leg drops is the big move that's going to end the match.

Downtime

Downtime is time that passes "off-screen" either between adventures or during parts of an adventure where nothing interesting enough to role-play is happening. If the GM says "After 3 days of travel, you arrive at the Cave of Doom," that's downtime. Characters can use downtime between (and sometimes during) adventures to engage in off-screen activities that aren't particularly compelling or exciting but that can nonetheless impact the on-screen story: building or modifying equipment, doing research, cultivating relationships, etc. As with adventures, the amount of game time that passes during a particular stretch of downtime varies according to the pacing of the story. The amount of downtime often decreases sharply as a story arc moves toward its conclusion, but there's usually a longer-than-average stretch of downtime between the end of one story arc and the beginning of the next.

Scene

A scene is a single unit of storytelling and typically involves a group of characters engaging in a particular activity in a single location. As with adventures, the amount of game time that passes during a scene varies according to the nature of the scene: a single combat scene may take an hour of real time but only a few seconds of game time, while a science montage may take several hours of game time even though the real-world resolution consists only of a single die roll and a brief description. Some scene changes--like when the players move to a new location or when a social interaction turns into a fight scene--are obvious. In the case of more subtle changes, the GM will often have to make a ruling on whether a particular change in the environment or action constitutes the beginning of a new scene. For scenes that don't have a clear endpoint, it's usually best to let the players decide how long they want to spend on a particular scene, with the GM only forcing scene changes when they need to create a sense of urgency or when a scene loses momentum because the players can't decide what to do next.

Turn

Turns tend to be used when characters are engaged in activity that's painted in broad strokes: searching rooms, mid-range movement, bypassing obstacles (picking a lock or disabling a trap, for example), working a crowded room to win goodwill or gather information, etc. Use turns when a round isn't long enough and an hour is too long. Turns often measures between-the-scenes activity that isn't downtime but isn't handled in enough detail to count as a scene: exploration, movement, and activities like foraging, research, or hunting that involve long stretches of waiting or tedium. Game effects (like how long the benefits of a spell or special ability last) are often measured in turns. There are 10 turns in an hour, so each turn represents about 6 minutes of game time.

Rounds

Rounds are used for combat and most action scenes where there is a flurry of fast-paced activity. A round represents the amount of time that it takes for every character in the scene to take an action. There are 10 rounds in a turn, which means that each round lasts around 30 seconds of game time.

Segments

Segments are subdivisions of rounds that are mostly used to track things like round-long effects, casting times for spells, and other rules-related durations. Each character's action during the round takes 1 segment, so the total number of segments per round depends on the number of characters involved in the scene. The first character acts on segment 1, the second on segment 2, and so forth. If an effect that lasts 1 round starts on segment 8, it ends on segment 8 of the following round. If the number of segments per round decreases (because characters have become incapacitated or left the scene), effects that are supposed to end or take place after the last segment go off at the end of the round in order from lowest to highest segment.