I saw such phrase "Fans have been shipping these two for years, and it’s easy to see why. They’re attractive, single, and they’ve got a lot in common..." in this article. What does "shipping" mean in this context?
To ship two people or characters, means wanting to see them in a (romantic) relationship. This is usually something fans of a show or other popular medium do.
In this sense, to ship two persons means to imagine that they are in a romantic relationship, or to desire that they are in a relationship. This normally applies to characters in a work of fiction (movie, novel, etc.), it would be unusual (but not impossible) to apply it to real people.
The term originates from fandom. It was popularized in the Internet era, so you won't find it in older dictionaries. Even today, it may not be known by all native speakers. It's still somewhat slang.
“Ship” in this sense is an abbreviation of relationship, it's unrelated to the “boat” meaning. There are derived expressions that make a pun (e.g. a “sailed ship” for an imagined relationship that has become a fact in the fictional world, e.g. by a later season of the series), but they are a lot less common than the simple verb.
The word is most commonly used as a verb, but it has some derivatives. “A ship”, in this sense, is the imagined relationship. A shipper is someone who likes to imagine such relationships.
See also the Wikipedia article on the topic.