In plain words
Actions do not bind one who has renounced them through yoga, whose doubts have been cut by jñāna, and who is self-possessed, Dhananjaya.
Word for word
Actions do not bind one who has renounced actions by yoga, whose doubt is cut away by knowledge, who is self-possessed, O Dhanañjaya.
The commentators
Bhagavadgītābhāṣyam
कस्मात् ? —
योगसंन्यस्तकर्माणं परमार्थदर्शनलक्षणेन योगेन संन्यस्तानि कर्माणि येन परमार्थदर्शिना धर्माधर्माख्यानि तं योगसंन्यस्तकर्माणम् । कथं योगसंन्यस्तकर्मेत्याह — ज्ञानसञ्छिन्नसंशयं ज्ञानेन आत्मेश्वरैकत्वदर्शनलक्षणेन सञ्छिन्नः संशयो यस्य सः ज्ञानसञ्छिन्नसंशयः । य एवं योगसंन्यस्तकर्मा तम् आत्मवन्तम् अप्रमत्तं गुणचेष्टारूपेण दृष्टानि कर्माणि न निबध्नन्ति अनिष्टादिरूपं फलं नारभन्ते हे धनञ्जय ॥ ४१ ॥
In plain words
Why? —
'One whose actions have been renounced through yoga' means someone who, through the yoga that is the vision of the highest truth, has, as a seer of that highest truth, let go of actions called merit and demerit. How does someone reach that state? Krishna answers: 'one whose doubt is cut off by knowledge' — by the knowledge that is the vision of the oneness of the Self and God, doubt is severed for such a person; that is what makes him one whose doubt is cut by knowledge. For such a person, self-possessed and undistracted, whose actions are renounced through yoga, actions seen simply as the movements of the guṇas no longer bind him; they no longer set in motion any fruit — undesirable or otherwise — Dhanañjaya.
Close to the Sanskrit
From what [cause]? —
'One whose actions have been renounced through yoga' — by yoga characterized as the vision of the highest truth, by whom, the seer of the highest truth, actions called merit and demerit have been renounced — him, 'one whose actions have been renounced through yoga.' How does one become such a one? He answers — 'one whose doubt is cut off by knowledge' — by knowledge characterized as the vision of the oneness of the Self and the Lord, doubt is cut off, for whom — he is 'one whose doubt is cut off by knowledge.' One who is thus one whose actions are renounced through yoga, him, self-possessed, undistracted, actions seen simply as movements of the guṇas do not bind; they do not set in motion a fruit in the form of the undesirable and the like, O Dhanañjaya.