This is most ofter used on tumblr by fandoms. Fandoms will ship everything and anything. Shipping comes from the word relationSHIP. Basically it is when you want a fictional character, real-life person, or cartoon people to be together. People often write fanfictions about their favorite ship, called their OTP.
Person 1: Wow I totally ship michellie!!
Person 2: OH MY GOD NO I SHIP DELLIE!!
Person 3: wait how can you ship a person isn't that illegal to send them with UPS or something?
Person 2: No i want them as a couple. It's called Shipping.