It’s a popular term in any fandom, not just with Otaku. What is Shipping?
The term Shipping is that act of putting two characters from a fandom together in a relationship. It is most often a romantic relationship, but can also be used for platonic relationships. This can be simply for fun, for fanfictions, fanart, or (for the Otaku out there) Doujinshi. Characters who are shipped can be of any age, gender, or even species — remember, this covers all fandom where there may be non-human characters.
“I ship Cloud with Yuffie.”
Those who do the Shipping often refer to themselves as Shippers. Believe it or not Shipping isn’t a new term, as the earliest known use online is from the early 90s, but it has been gaining a lot of popularity in recent years.
And that’s all you need to know about Shipping. You can find more information on subculture terms just like this in my growing Otaku Encyclopedia.