"Shipping" is a fandom term that originated from the phrase "relationship shipping." It refers to the act of supporting a romantic pairing between two fictional characters, often from books, movies, or television shows.
Harry and Ginny are two prominent characters in the Harry Potter series. Their relationship develops over the course of the books, culminating in their marriage in the final book, "Harry Potter and the Deathly Hallows."
So, "shipping Harry and Ginny" means that a fan supports the idea of Harry and Ginny being together romantically. This support can be expressed through fan fiction, artwork, discussions, and other forms of fan engagement.