Private fares or unpublished fares (also known as a consolidator or bulk fares) are prices for air seats that are not listed anywhere online, be it an airline website or OTA. Air consolidators get these concealed discounted fares from airlines, add a markup, and pass them on to retailers (travel agents).
Such fares can be part of a purposefully vague advertisement like “best prices” or “cheapest” tickets — without mentioning precise figures, sold as part of a package, or shared over the phone. Private fares offer the best savings on international flights, business/first-class seats, last-minute purchases, and one-way tickets. However, their trade-offs include high cancellation penalties, issues with loyalty programs, and a number of restrictions (e.g., such tickets are often nonrefundable, non-exchangeable, etc.).