The term typically refers to a modified version of an existing application. In the context of a "Pro" version, this usually means a developer or third-party has unlocked premium features that are normally behind a paywall. F-Droid for Android - Download the APK from Uptodown

You can browse and download any app anonymously without signing into a Google account. Understanding "Mod APK (Pro)" Files

While there is no single app simply named "F," the version number and the "Pro" designation are frequently associated with the F-Droid ecosystem or specific modified "Pro" versions of utility and media apps distributed as APKs. F-Droid: The Privacy-First Android Hub