Lineage is important. It is important in many things and it often gets brushed over, but lineage plays a special significance in the transmission of the Buddha's teachings.
Lineage ensures a living transmission. It ensures communication on a personal level, heart to heart, mind to mind.
Lineage is most often traced through one's root teacher. We all have many teachers in life, but one's root teacher is the one that introduces us to our own nature of mind. This direct introduction to our own buddhanature is what forms the basis of our path. We walk the path infused with their blessings.
My own root teacher is Younge Khachab Rinpoche. Rinpoche trained with many teachers in the monastic tradition as a child, but it wasn't until he met and trained under the Dzogchen yogi Dingri Khenchen that he experienced the subtlety and profundity of the nature of the mind.
Dingri Khenchen was a great scholar and teacher at Dzogchen Monastery in his youth and spent the great part of his life in secret retreat. He was affectionately called grandfather by everyone but he was a realized practitioner and scholar.
Dingri Khenchen was a student and disciple of the great Khenpo Kunzang Palden (Khenpo Kunpal). Khenpo Kunpal was one of the foremost holders of the Longchen Nyingtig lineage and was renowned for being a great practitioner and scholar.
Khenpo Kunpal was the disciple of Patrul Rinpoche, the wandering yogi and preeminent Dzogchen master. Patrul Rinpoche's root teacher was Jigme Gyalwe Nyugu, who was the main disciple of Jigme Lingpa.
That is the close lineage, close in the sense that you can still feel their warmth. The extensive lineage can be traced all the way back to the Buddha through the succession of teacher and student.
One heartfelt connection at a time, for thousands of years.