Harmonic chanting is that amazing deep, vibrating chanting that Tibetan monks do. Tibetans developed their own complex multinote chanting after learning a similar style from Mongolians who invaded Tibet in the time of Ghengis Khan. Mongolians call that kind of sound throat-singing.
The Mongolians became staunch Tibetan Buddhists in addition to their own native shamanic religion, which was a lot like the native shamanic religion of Tibet. Mongolia and Tibet have remained culturally linked ever since.
Harmonics are the extra sounds an octave above and/or below a musical note that is sung or played. The many styles of Mongolian throat-singing can produce two to three notes with one person's voice. The Tibetan monks developed a way to produce four notes at once.
You have probably heard harmonic chanting whether or not you realize it. If not, I recommend listening to one of the CDs of the Drepung Lamas chanting. To me they are the very best at the Tibetan style.
Also recommended are any recordings of David Hykes (especially Wind Horse Riders), the Harmonic Choir, or the Tuvan musical group Hun Huur Tu.
Tuva is a tiny country between Mongolia and Siberia that hosts a world champion throat-singing competition. It was made famous by a book called Tuva or Bust and by a documentary film about the competition, called Ghenghis Blues. The film (available on DVD) and its soundtrack CD are also highly recommended.