Hochgeboren is a form of address for members of the highest German nobility. It translates to High Born or of High Birth.
The actual address is "Euer" Hochgeboren. It is the correct form of address for German high nobility: princes, dukes, and counts.

The title should not be confused with (Euer) Hochwohlgeboren

Hochwohlgeboren

Hochwohlgeboren is a form of address for members of the lower German nobility or landed gentry. The English translation is High Well Born.-German usage:...

, which ranks lower, and is the correct form of address for German barons, knights, and Freiherren; or (Euer) Wohlgeboren, which ranks lower than Hochwohlgeboren, and is the address for a Vogt

Vogt

A Vogt ; plural Vögte; Dutch voogd; Danish foged; ; ultimately from Latin [ad]vocatus) in the Holy Roman Empire was the German title of a reeve or advocate, an overlord exerting guardianship or military protection as well as secular justice...

or Büttel.