|You know it makes sense|
The episode "Parallels" (TNG) is based on the Many-Worlds Interpretation (MWI) of quantum mechanics. This is an important, but controversial, theory in modern physics. It's one of the ways of making sense of quantum events. Basically, MWI means that at every moment the universe is splitting into different versions, or "worlds", according to the different outcomes of quantum events. The theory was proposed in 1957 by a physicist named Hugh Everett, but it was largely ignored till rather later.
MWI means that everything that can happen, does happen—in some world. (Some outcomes are more likely than others however.) This includes different outcomes at every level. In this world you are reading this page. However, there is a world where you have gone to have a cup of coffee. Perhaps you don't drink coffee, but there's a world where you do. There is also a world where the page says something quite different, or where it doesn't exist. On a larger scale, there is a world where the Soviet Union still exists, and a world where the atomic bomb was never invented, and a world where the American Revolution failed...
Incidentally, in TOS the Enterprise encounters several alternate Earths, which are not different timelines but rather Earth-duplicate planets where history took a different turn at some point. You can argue that this is scientifically implausible (assuming that these planets are all relatively close to Earth rather than somewhere in an infinite universe) but for the 1960s audience it was probably better than trying to explain completely unfamiliar ideas about diverging timelines.
Well, back to TNG. Worf gets somehow disconnected from his own world and goes drifting across realities. At first the changes are small. He is at his birthday party, and there is a chocolate cake—but then it is yellow, some other flavour. But they gradually get bigger, and the events he remembers are more and more different from the ones everyone else remembers. The divergences grow to different political alignments, different family members, and ultimately an Enterprise in a hopeless situation, a history in which the Federation has lost the struggle with the Borg. This last case is a "Kobayashi Maru" test on a grand scale. In Star Trek 2: The Wrath of Khan Kirk commented on this test of a no-win situation that "How we face death is at least as important as how we face life." By this standard, the alternate Enterprise doesn't do very well, actually. Although there are bigger and bigger changes, to indicate increasing divergence from where Worf started, there are also random small changes. (There's a page on this site which discusses the logic of the progressively greater divergences.)
This makes a superb episode, but the writers evidently couldn't see much more scope (unless they had gone for alternate-world stories like the alternate-Earths of TOS), since it doesn't appear again. In "Parallels", apart from the interest of the concept itself, the main theme is Worf being parachuted unexpectedly into a relationship with Troi. It sometimes surprises people who aren't familiar with SF that there are a lot of distinctively SF love stories. This is a good example. Worf sees Troi as a close friend, but that's all. But in the world he arrives in, Troi is his wife. From her point of view, they have a deep relationship of several years' standing. There is a moving scene where Worf is in despair that no one believes him and he doesn't know what to do. Troi tells him: "Whatever's wrong, whatever happened, I want you to know that I believe you. And that I love you. And together we'll find out what's happening." They do find out, and as a result Troi has to say goodbye to Worf as he sets off back to his own world.
In light of Worf and Troi's relationship later in the episode, some details earlier in the episode take on extra significance. There is a little extra affection in Troi's manner at the party—look when she kisses Worf, and the way she laughs when he avoids the question of his age. Also watch her manner in the scene in Ten-Forward where Worf asks her to be Alexander's "soh-chim". They are just friends, but the progressive shift toward a closer relationship is already starting. This is a subtle performance: Marina Sirtis was sometimes limited by her material but when given the chance is superb.
It's hard to see how the "Parallels" concept could be made to look compatible with the usual approach of a single timeline, and Star Trek wisely didn't try.
As a result of this experience, Worf decides to explore a relationship with Troi in his own world. (This happens mostly after "Parallels".) This was apparently unpopular with the fans, who favoured Troi getting back together with Riker, but I have always preferred it. Consider the scene just mentioned. It's hard to think of a comparable Troi-Riker moment showing, not hot romance, but depth of connection. Riker represents the superficial attraction. Worf represents something less obvious but more profound. Troi-and-Riker is like one of those romantic comedies where the hero eventually gets the woman who for no apparent reason he adores. Troi-and-Worf, on the other hand, is like Jerry Maguire, where the parties eventually choose someone who doesn't immediately drive them wild but who completes them at a deep level. "You had me at Qapla."
"Parallels" is an episode that combines a fascinating science-fiction premise, brilliantly developed, with a character story which follows from it. It suggests reflection on paths not taken, something most people wonder about from time to time.
 At quantum level, things exist in a state of fuzzy "superposition" but when measured you get a definite result—though you can't measure everything at the same time. The standard interpretation is the Copenhagen Interpretation, in which the uncertainty "collapses" when measured. This works well but leads to messy implications (look up Schroedinger's Cat). The Many Worlds Interpretation, or MWI, is that all the possibilities exist, but in different realities. There is lots of accessible material on the issue online. It is generally held that it would be impossible to move to, or observe, another quantum reality in the way Worf does in the TNG episode, but in science fiction this can of course be disregarded. [Return]
 What "more likely" means in the context of MWI is a bit of a problem. Concepts like "measure of existence" have been suggested. [Return]
 Marina Sirtis, who played Troi, has been quoted as saying that the problem with the Troi-Worf relationship was that it tended to make Worf a softy, drawing him away from his Klingon character. By contrast his relationship with Dax in DS9 did not have this problem, as viewers will recall. This is a fair point but the problem was not necessarily insoluble. [Return]