A very insufficient and quick description of what a Gestalt is:
Every melody consists of notes. Transpose it and you have other notes, but still the same melody. It is the Gestalt of the respective melody.
Harmonic Gestalt is even easier to understand. If you hear a minor scale, you know what’s up. The notes can change or there can only be a few notes from the scale in the air – still you’d hear the Gestalt of “minor”.
Christian von Ehrenfels is one of the key figures of the Gestalt Theory.
Learn more on the homepage of the Society for Gestalt Theory and its Applications.