Where the greater is, the lesser ceases. This famous Latin phrase of uncertain origin simply means that where one with greater authority is present, the power of the lesser ceases. So it's essentially a phrase that emphasizes respect for hierarchy, whether it be a superiority of role, seniority, or athleticism. It's also used to justify a choice that protects a greater good over another. In the legal context, it's used when a superior source prevails over an inferior one.