In plain words
Therefore always perform the action that ought to be done, without attachment. By acting without attachment, a person attains the highest.
Word for word
Therefore, unattached, always perform action that ought to be done; for, performing action unattached, a person attains the highest.
The commentators
Bhagavadgītābhāṣyam
यतः एवम् —
तस्मात् असक्तः सङ्गवर्जितः सततं सर्वदा कार्यं कर्तव्यं नित्यं कर्म समाचर निर्वर्तय । असक्तो हि यस्मात् समाचरन् ईश्वरार्थं कर्म कुर्वन् परं मोक्षम् आप्नोति पूरुषः सत्त्वशुद्धिद्वारेण इत्यर्थः ॥ १९ ॥
In plain words
Because this is how it is —
So: unattached — meaning free of any clinging. Constantly — meaning always, with no time left out. The work to be done — meaning the standing duty that is yours and not optional. Perform it — meaning carry it through to the end. Because a man who acts this way, unattached, doing the work for the Lord's sake, reaches the highest thing there is: liberation. Purity of mind is the door he goes through. That is the sense of it.
Close to the Sanskrit
Since this is so —
Therefore, unattached — that is, free of clinging — constantly, that is, at all times, the work that is to be done, that is, the obligatory standing action, perform, that is, bring to completion. For, since a man performing it unattached, doing the action for the sake of the Lord, attains the supreme, liberation, by way of purity of mind — this is the meaning.