TPDD (Temporal Plane Destruction Device, or Time Plane Destruction Device) is a device used by a time traveler that acts as a time machine. It has the ability to bring one back and forth in time. Although this isn't the best method of time traveling, it successfully transfers the beings whole. Mikuru Asahina was the first to introduce the TPDD which she wouldn't let Kyon see because it was classified information. Future Mikuru reveals the full name of the device in the Disappearance arc.
Every time the TPDD is used, it punches a hole in the time plane. The further the travel to the past, the more damage is dealt, along with the greater number of trips. The "holes" need to be filled afterward or they will affect the future. The main task of time travelers in the past is to repair TPDD errors, but Mikuru Asahina is an exception.
Mikuru says that all time travelers have it or do not depending on whether it was predetermined they should, explaining her sudden recovery of it after her older self took it in Bamboo Leaf Rhapsody. Future Mikuru later tells Kyon that the TPDD is connected to the information in her head.
The theory behind the TPDD was invented (in the future) by Haruhi Suzumiya and a neighbor of hers, known in the present only as the Bespectacled Boy. This boy was marked for death by a faction of time travelers including Fujiwara, but was rescued by Mikuru and Kyon. The boy made his contribution to the theory after seeing the ripples made by a turtle in water (placed there by Kyon, at the behest of future Mikuru, thereby creating a time loop).
According to Fujiwara, he uses the same sort of time travel technology as Mikuru Asahina.