Out of compassion for them alone, I dwell within their own heart and destroy the darkness born of ignorance with the shining lamp of knowledge.
Explanation
Krishna continues from the previous verse, where he says he gives devoted people the yoga of understanding (buddhi-yoga). Here he explains that, out of compassion (anukampā), he abides in their inner self (ātma-bhāva) and removes the darkness born of ignorance (ajñāna) with the bright lamp of knowledge (jñāna). Commentators differ on whether ātma-bhāva means the devotee's own heart or mind, or the state of the Self, but all agree that the knowledge is a grace that comes through devotion.