Shipping, or more properly 'ship (shorthand for relationship), is a romantic pairing between two or more characters. A fan of such a pairing is known as a shipper. Shippers are of the opinion that particular characters are romantically right for one another, and thus support the ship .Shippers often write fanfiction entirely about their chosen ship being romantic, although sometimes ships are merely background to the larger story of the fanfic. A common ship in the South Park fandom, for instance, would be Stan/Kyle (also known as Style).
Of all the obsessions that universally afflict fandoms, Shipping is by far the most persistent, widespread and prone to be taken seriously. It is common in all realms of fiction to devote at least some time to tying up the romantic relationships of characters - even South Park itself has devoted episodes due to romantic plotlines, though few - and as a result, almost all fiction focused on human or human-like beings either contains relationships in canon, or in its own fanon. It is also somewhat more common for even well-meaning or otherwise polite fans to be reflexively defensive of their ships, often taking personal offense when another user discusses it in a negative or even sometimes neutral light.
Canon and authorial intent do not often dictate people's shipping preference. You'd be hard-pressed to find anything that honestly puts any sort of restraint on shipping preference. Characters will often be shipped with little or no regard to their ages, sexualities, canon relationships (even familial), age gaps, or origins. Crack pairings are often denote for those that contain no basis or are implausible by a design.
In South Park
Some shows are made to be deliberately enticing to shippers, but for the most part any relationships in South Park are merely suggested, at best. The main characters are all eight to ten years old or adults, and many of them are male. What little romance does occur within the series is often relegated to either Stan and Wendy's relationship, a long-running plot thread since the series' first season, or those between the children's parents, such as Randy and Sharon. The majority of relationships in the series rarely last longer than a single episode. As a result, some South Park fans criticize shipping culture, though it continues to be the dominant force in the fandom.
Some fans see the Season 16 (2012) episode "Cartman Finds Love" a deliberate satire against shipping culture, including that of the show's own fandom, though Trey Parker and Matt Stone have never referenced shipping in an audio commentary or interview to date.
There's a whole nomenclature dedicated to quick, easy and unique ship naming. The most basic tool of communication here is the slash — if you wanted Stan and Kyle to get together you could always say you shipped Stan/Kyle. However, for the South Park fandom, that's just not exotic enough. We will not be content with anything less than a short, sweet and catchy brand name, the better. Shipping culture has imported the Portmanteau Couple Name from various Japanese anime fandom; apart from its infamous usage in the gossip industry (for example, "Brangelina", "Bennifer", "TomKat") you can find people online declaring themselves fans of "Style", "Kyman", "Creek", "Candy" and "Dip". Yes, Dip.
Nature of Shipping
Shipping is often about the anticipation. Paragraphs and essays and counter-essays weighing megabytes at dozens of pages will be written about who will get together, who should get together, and what the disciplines of political science and feminism and probability theory have to say about the issue (the above is not hyperbole). People will argue endlessly about the romantic future of nearly any given ensemble, but if that point should actually be resolved, the discussions will basically go through a round of ranting and gloating and then unceremoniously run out of steam.
That's probably because anticipation is something that is easy for a reader to feel a part of, even if the anticipation is for something fictional. Real life romance, for all its shortcomings, actually happens for us: We move on from looking forward to something great to experiencing something great (or at least we can hope). Being in a romantic relationship and reading or writing about a fictional romantic relationship are very different things, much more different than looking forward to each of those respectively. The contrast is jarring — once a part of this great love story, and now no longer. This can lead to disillusionment, often leading to moving on to new fandoms.
Shippers have a reputation of insane devotion to their One True Pairing and of interpreting the tiniest, most ambiguous details as evidence. That much is clear by the prevalence of Shipping Wars in any fandom discussion. In some extreme cases they will freely admit to actively rooting for sympathetic characters to suffer or die just to get them out of the way, or believe the show's creators intentionally hide evidence as subtle hints towards non-canon ships. A very small handful of shippers sometimes enter fandoms out of love/interest in the shipping aspects of the fandom rather than a true interest in the source material as well.