An ulterior interest, argument, or revelation is one you try to keep hidden, like your ulterior motive for weeding your grandmother's garden is to have a conversation with your crush — and Grandma's neighbor — who happens to be outside, too.
The adjective ulterior is a Latin word which means “more distant” or “future.” Something that is ulterior may lay the groundwork for what comes later, like a new friend who hangs out with you at your house but whose ulterior motive is to date one of your siblings, or the incredible popularity of a series of novels set in a real place having the ulterior consequences of that place becoming a tourist destination.