In plain words
But one who moves among sense objects with self-governed senses, free from attraction and aversion, and with oneself disciplined, attains inner clarity.
Word for word
But moving among objects with senses free of attraction and aversion and under his own control, the one whose self is governed attains serenity.
The commentators
Bhagavadgītābhāṣyam
सर्वानर्थस्य मूलमुक्तं विषयाभिध्यानम् । अथ इदानीं मोक्षकारणमिदमुच्यते —
रागद्वेषवियुक्तैः रागश्च द्वेषश्च रागद्वेषौ, तत्पुरःसरा हि इन्द्रियाणां प्रवृत्तिः स्वाभाविकी, तत्र यो मुमुक्षुः भवति सः ताभ्यां वियुक्तैः श्रोत्रादिभिः इन्द्रियैः विषयान् अवर्जनीयान् चरन् उपलभमानः आत्मवश्यैः आत्मनः वश्यानि वशीभूतानि इन्द्रियाणि तैः आत्मवश्यैः विधेयात्मा इच्छातः विधेयः आत्मा अन्तःकरणं यस्य सः अयं प्रसादम् अधिगच्छति । प्रसादः प्रसन्नता स्वास्थ्यम् ॥ ६४ ॥
In plain words
So we have now seen the root of every kind of ruin: brooding on sense-objects. Having covered that, here is what causes liberation —
'Released from attachment and aversion' — because ordinarily, the senses move toward their objects driven precisely by attachment and aversion. Among people at large, someone who is genuinely seeking liberation moves through the world, meeting the unavoidable objects of hearing and the other senses, but with senses that are no longer ruled by attachment and aversion — senses that have instead come under his own control. That is what 'one whose self is governable' means: someone whose mind, responsive to his own will rather than driven by craving, has become obedient. Such a person attains prasāda — inner tranquility, that clear, settled well-being.
Close to the Sanskrit
The root of every calamity has [now] been stated: brooding on sense-objects. Now, at this point, this cause of liberation is stated —
'Released from attachment and aversion' — attachment and aversion, [together] attachment-and-aversion; for the activity of the senses is naturally led by these. Among such people, whoever is a seeker of liberation, he, with senses — hearing and the rest — released from those two, moving among, encountering, unavoidable objects, with senses that are 'under the control of the Self' — that is, his own controllable senses, senses that have become controlled, by those senses under the control of the Self — [is] 'one whose self is governable': governable at will, [that is,] whose self, [meaning] the mind, is governable — he, this one, attains 'tranquility.' 'Tranquility' [means] clarity, [inner] settledness. [End of commentary on verse 64.]