What is this system of reincarnating lamas or teachers?

The system of recognizing reincarnate lamas, called tulkus, was started from Karmapas, it comes from the Karmapa’s lineage; this is generally known.

And particularly the third Karmapa, Rangjung Dorje – when he was recognized by someone else as the Karmapa, he was the first tulku who was recognized in the system of recognizing tulkus that is prevalent now.

HH, 17^th Karmapa
Ogyen Trinley Dorje

From Kamashila
Short-Ngon-dro teaching
Germany, 2014