In plain words
Established in yoga, perform action, Dhananjaya, abandoning attachment and remaining equal in success and failure. Such equanimity is called yoga.
Word for word
Abiding in yoga, perform actions, abandoning attachment, O Dhanañjaya, having become even in success and failure; evenness is called yoga.
योगस्थः कुरु कर्माणि सङ्गं त्यक्त्वा धनञ्जयसिद्ध्यसिद्ध्योः समो भूत्वा समत्वं योग उच्यते
Other commentaries
The commentators
▸Bhagavadgītābhāṣyam
यदि कर्मफलप्रयुक्तेन न कर्तव्यं कर्म, कथं तर्हि कर्तव्यमिति ; उच्यते —
योगस्थः सन् कुरु कर्माणि केवलमीश्वरार्थम् ; तत्रापि ‘ईश्वरो मे तुष्यतु’ इति सङ्गं त्यक्त्वा धनञ्जय । फलतृष्णाशून्येन क्रियमाणे कर्मणि सत्त्वशुद्धिजा ज्ञानप्राप्तिलक्षणा सिद्धिः, तद्विपर्ययजा असिद्धिः, तयोः सिद्ध्यसिद्ध्योः अपि समः तुल्यः भूत्वा कुरु कर्माणि । कोऽसौ योगः यत्रस्थः कुरु इति उक्तम् ? इदमेव तत् — सिद्ध्यसिद्ध्योः समत्वं योगः उच्यते ॥ ४८ ॥
In plain words
If the one driven by the fruit of action is not the one to do the action, then how is it to be done? That is the question. The answer is this —
Standing firm in yoga, act — but act solely for the sake of Īśvara; and even there, act with nothing more than the thought 'may this please him', having let go of attachment altogether, Dhanañjaya. When an action is done free of craving for its fruit, one outcome is success — born of an inwardly purified being, marked by the attainment of knowledge — and the other is failure, born of the opposite. Toward both of these, success and failure alike, remain even, the same, and only then act. So what exactly is this yoga Kṛṣṇa told Arjuna to stand established in before acting? Here is the answer, precisely: evenness of mind toward success and failure — that is what is called yoga.
Close to the Sanskrit
If action is not to be done by one impelled by the fruit of action, then how is it to be done — thus the question; it is said —
Being established in yoga, perform actions solely for the sake of Īśvara; there too, with the thought 'may Īśvara be pleased with me' — having abandoned attachment, O Dhanañjaya. When action is performed devoid of craving for its fruit, [there is] success — born of the purity of one's inner being, characterized by the attainment of knowledge; [there is also] failure, born of the opposite of that; with respect to both of these, success and failure, being equal, the same, perform actions. What is that yoga, established in which, [Kṛṣṇa] said, 'perform'? This very [thing is] that — equanimity in success and failure is called yoga.
▸Gītā Vāhini
అంతటితో వదలక “కర్మయోగికి సంఘబుద్ధి కంటే, సమబుద్ధి ప్రధానము”ని కూడనూ అన్నాడు. సంఘబుద్ధి వద్దన్నాడు; ఎందుకన, బంధనమునకు మూలకారణము సంఘమే. “ఈ కర్మ నాది, ఈ చేసే కర్మఫలము నాది. ఈ కర్మకు కర్త నేనే” అను సంఘము బంధమునకు గురి అగును.
సంఘబుద్ధికి అతీతుడయిన మంచిదన్నాడు, కృష్ణ పరమాత్మ. “సమత్వమే యోగ”మన్నాడు. అందుకనే కృష్ణపరమాత్మ “సమత్వం యోగ ఉచ్యతే” అని అన్నాడు.
In plain words
Not stopping there, Kṛṣṇa also said: "For the karma yogī, the attitude of evenness matters more than the attitude of attachment." He said the attitude of attachment is not wanted. Why? Because attachment itself is the root cause of bondage. The attachment that says, "This karma is mine, the fruit of this karma I am doing is mine; I alone am the doer of this karma," falls into bondage.
Kṛṣṇa Paramātma said it is good to rise beyond the attitude of attachment. He said, "Equanimity itself is yoga." That is why Kṛṣṇa Paramātma said, "Samatvaṃ yoga ucyate."