What do you mean by 'shipping', I'm unfamiliar with this term.
I'm not sure why we use the term "ship" in this sense, but "shipping" characters is basically what characters you think make the good couples. For example, I don't ship Severa with most of the guys (exception being Laurent) cause most of her convos are usually her spitting venom and being cynical and rude till she does a mandatory 180 during the A or S supports and it comes across as really forced in my eyes. However I ship her and Noire due to the fact that she is one of the few people that Severa actually starts off somewhat nice too. Then after their supports and extra convos that they have during the extra content, I could see those two being a couple.
I'm sure someone else can explain it better --- PSN:Korius Steam ID: Korius Currently Playing: TF2, Mighty Switch Force HD, MH3U
The term "shipping" derives from the word "relationship", as I understand it; it basically means "I think Character X and Character Y would make a good couple, and I am expressing my desire for them to hook up romantically." --- Official Bride and Wife of Noire (of the Fire Emblem Awakening message board)