A plus-one is the extra person you may bring to a party, wedding, or dinner when the invitation is for you and one other guest — but that other person is not named on the card. The host is saying, in a polite, slightly stylish way: you may come with someone. That someone is often a partner, but it can be a friend, a sibling, anyone you choose; the point is the seat, not who sits in it. People use it as a noun ("I'm bringing a plus-one") and, more loosely, for the whole idea ("Do we get a plus-one?"). It belongs to informal social English, especially around weddings and work events. Though actually, it is not a promise that every invitation works this way: some cards say "plus-one", some name both people, and some mean you only. If nobody offered you one, bringing an extra guest can look rude, not generous.