Gilgul, rolling or cycling, is the kabbalistic doctrine of reincarnation, first found in the Bahir. Souls return in new lives to fulfil commandments left undone or repair past wrongs. Lurianic Kabbalah elaborated the idea, tracing the roots and sparks of souls through generations.
Gilgul
The transmigration of souls in Kabbalah, by which a soul returns to complete its repair.
Also: gilgul neshamot, reincarnation