Plot Threads

Some narratives will have the focus follow The Hero and his merry band of stalwart allies from their first meeting all through to the end. However, that's not to say that events only occur in the hero's vicinity, as if the world were completely inert save for their actions; or that there is only one Story Arc being told throughout the narrative. Therefore, some authors choose to show a wider range of action by alternating focus on the various groups of characters who deal with their own contributing story threads that weave back into the greater narrative.

These are called Plot Threads, and this is their trope.

When writing an episode, book, or anthology, authors may work multiple plotlines into the action as Plot Threads. These can range from episodes with a specific Character Focus, to having alternating chapters in a book advance a separate (yet related) plotline, and having the same cast deal with various problems simultaneously. Commonly, these various plots vary in terms of time/space devoted to them, and their importance to the overreaching Myth Arc.

There are many different variations. Often the A plot will simply be a short bit at the beginning of the episode that gets the characters into "wacky situations"—it triggers the B and C plots. Sometimes the plots are nested like Russian dolls, and to solve the A Plot the B and C Plots must be solved first. Some stories have them all go on simultaneously, and the action cuts back and forth between them. The number can vary, too. Sometimes there's just the main plot and the secondary. Three seems to be the most common number. Why? Who knows, maybe the Rule of Three. Sometimes there's four or even more, but that tends to be pretty rare, mostly due to time and focus constraints.

A given work may also vary the number of ongoing plot threads within itself. A show with a Kudzu Plot will introduce new plots at the same rate they are solved. Others will have episodes with 1, 2, or 3 plot threads in a given season, depending on the tone they try to set for the episode.

Speaking of tone, this can vary depending on the number of Plot Threads. Generally, the fewer threads there are, the more intimate the focus will be. The characters will rarely split up, and if they do the focus will always be on the lead. Whatever else is going on in the setting outside of the POV character's line of sight will only be seen via Flash Back, Monologue, or other narrative devices. This style tends to favor Action, Mystery and Suspense, we only know what our brave hero does, after all.

Two plot threads allows for a wider, dual narrative that broadens what the viewer knows about the drama and setting, better allowing things like Dramatic Irony. For example, if the gang chooses to split up, you'll have the POV follow each as they investigate, so we the audience know more than the characters do... at least until they reunite and compare notes to discover it was old man Withers with glow in the dark paint. At it's most extreme, the action may follow two completely separate POV characters, cutting to and fro.

With three or more plot threads, you usually get a lot of complexity and energy in a story, but the pacing becomes slower. This style tends to favor Drama and other genres with stories that have a large and diverse cast. You see it very commonly in animated shows and Dom Coms because of their serial nature, likewise Soap Operas and Long Runners will adopt this format because it tends to drag out the action and keep the viewers coming back.

Multiple plot threads are necessary for a Plot Parallel. In this instance, the two story lines mirror one another, each propping the other up. Also common in a Double Aesop.

Examples of works that have more than two plot threads

Anime and Manga

Inuyasha does this to the point of being mildly annoying, following not only the five main characters, but later on Naraku and all of his incarnations, Sesshomaru, Kikiyo, and other minor characters.
Gundam Seed and its sequel series, Destiny Does this to the point where we hardly ever see the two main characters in some episodes.

Literature

The Lord of the Rings employed this trope, giving it a place in one of literature's modern classics.
A Tale of Two Cities switches back and forth between London and Paris like this.
The Wheel of Time will be running at least a dozen at any given time after book 3.
The Deryni novels have anywhere from two to five plots going at one time, with more plots splitting off during wars (such as the Mearan campaign in The King's Justice) and other periods of high tension.
Warrior Cats generally swaps between two major plot threads, and a third, far-removed one.
Demi-Gods and Semi-Devils is a Wuxia novel with four different plots and main characters.

Live-Action TV

For the first five seasons and first half of the sixth season, the average episode of The West Wing had three or four plotlines. Generally, one was a political plotline, and the other three were either two "personal" plotlines (about the feelings or personal problems of one or more of the characters) and one silly plotline (usually involving someone - most often Donna or a special interest group - arguing or expressing deep anxiety about something comically trivial) or one personal plotline and two silly plotlines.
The Wire had many densely-interwoven plot-threads that coalesced towards the end of each season.
Heroes Volume 1 has about nine different plot threads, essentially one for each main character. They frequently weave together and diverge again as the characters interact with each other throughout the episodes, until all threads merge together for the grand finale.

Most Volumes of Heroes employed this technique, Generations and Redemption in particular, with there being a loose main arc the others eventually converged on.

Almost every episode of Seinfeld's later seasons involved multiple plot threads. Frequently, the ending of the episode would tie these threads together (very comically).

Theater

Older Than Steam: The Merchant of Venice, with its alternation between Venice and Belmont.

Video Games

Final Fantasy VIII Has the dream sequences, which turn away from Squall and the SeeD to give the player the chance to see Laguna's story from his days as a Galbadia soldier with a crush on Julia to his days with Raine and rebellion in Esthar.
Final Fantasy: The 4 Heroes of Light on the DS is all about this trope. The game frequently splits between the titular heroes (usually in pairs) as they make their way around.
This was the way that Final Fantasy VI handled having a cast of 14 major playable characters, with four major characters being playable at any one time.
Front Mission games often have a second campaign for the opposing side. Front Mission 4 switches back and forth between 2 groups the player controls.
Dragon Quest IV, dubbed "Chapters of the Chosens", narrates four different stories involve seven supporting characters who have their own quests and goals. You have to play through their chapters before the main hero/heroine recruits them in Chapter 5.
Fire Emblem Radiance Dawn has multiple acts, each follows different heroes/heroines and their armies. This causes the series' regular premise of Loads and Loads of Characters to be turned Up to Eleven.
Super Robot Wars sometimes does this for the sake of replayability. You may choose to play as one of the two or more different characters that aren't even related or related but get separated after the prologue. They also usually put plot points where the hero's team has to split up to do different missions in the different locations, but you may only follow one group at a time.
The Uncharted series does this in every incarnation except for the first game, though it always follows Nate, just at different points in time.

Web Comics

Captain SNES has more than ten concurrent plotlines. Even this episode doesn't list them all, as there is also (among others) the subplot of Chrono Trigger characters trying to find Marle, whatever happens to Max Force and plotlines introduced during the Nexus City arc later.
At one point, Homestuck collects so many plot threads that an omniscient character busts up a scrapbook containing clippings from the entire story and we spend around 150 pages jumping from character to character tying everything up like crazy in order to get everything ready for the massive End of Act 5 animation.

Western Animation

The Avengers: Earth's Mightiest Heroes has several running at once. As of "The Widow's sting" we have: The breakout, the Kree-Skrull war, the Secret Invasion, Kang about to come from the future, the assembling of the Masters of Evil, the creation of the cosmic cube, Hydra's re-emerging, Widow's Heel Face Turn Face Heel Turn The Mole whatever she really might be, and probably more.