Refers to one's total physical and mental energy, often used in contexts of exhausting or pouring all one's strength into something. Common in set phrases like 精根尽きる (to be completely exhausted) and 精根を傾ける (to devote all one's energy).
After a long battle with illness, he was completely drained of energy.
Etymology
Compound of 精 (spirit, energy) and 根 (root, stamina). The exact historical derivation is uncertain, but the combination naturally conveys the idea of fundamental energy or life force.