In plain words
These bodies of the eternal, indestructible, immeasurable embodied one are said to have an end. Therefore fight, Bharata.
Word for word
These bodies of the eternal, indestructible, immeasurable embodied [one] are said to have an end; therefore fight, O Bhārata.
The commentators
Bhagavadgītābhāṣyam
किं पुनस्तदसत् , यत्स्वात्मसत्तां व्यभिचरतीति, उच्यते —
अन्तः विनाशः विद्यते येषां ते अन्तवन्तः । यथा मृगतृष्णिकादौ सद्बुद्धिः अनुवृत्ता प्रमाणनिरूपणान्ते विच्छिद्यते, स तस्य अन्तः ; तथा इमे देहाः स्वप्नमायादेहादिवच्च अन्तवन्तः नित्यस्य शरीरिणः शरीरवतः अनाशिनः अप्रमेयस्य आत्मनः अन्तवन्त इति उक्ताः विवेकिभिरित्यर्थः । ‘नित्यस्य’ ‘अनाशिनः’ इति न पुनरुक्तम् ; नित्यत्वस्य द्विविधत्वात् लोके, नाशस्य च । यथा देहो भस्मीभूतः अदर्शनं गतो नष्ट उच्यते । विद्यमानोऽपि यथा अन्यथा परिणतो व्याध्यादियुक्तो जातो नष्ट उच्यते । तत्र ‘नित्यस्य’ ‘अनाशिनः’ इति द्विविधेनापि नाशेन असम्बन्धः अस्येत्यर्थः । अन्यथा पृथिव्यादिवदपि नित्यत्वं स्यात् आत्मनः ; तत् मा भूदिति ‘नित्यस्य’ ‘अनाशिनः’ इत्याह । अप्रमेयस्य न प्रमेयस्य प्रत्यक्षादिप्रमाणैः अपरिच्छेद्यस्येत्यर्थः ॥
ननु आगमेन आत्मा परिच्छिद्यते, प्रत्यक्षादिना च पूर्वम् । न ; आत्मनः स्वतःसिद्धत्वात् । सिद्धे हि आत्मनि प्रमातरि प्रमित्सोः प्रमाणान्वेषणा भवति । न हि पूर्वम् ‘इत्थमहम्’ इति आत्मानमप्रमाय पश्चात् प्रमेयपरिच्छेदाय प्रवर्तते । न हि आत्मा नाम कस्यचित् अप्रसिद्धो भवति । शास्त्रं तु अन्त्यं प्रमाणम् अतद्धर्माध्यारोपणमात्रनिवर्तकत्वेन प्रमाणत्वम् आत्मनः प्रतिपद्यते, न तु अज्ञातार्थज्ञापकत्वेन । तथा च श्रुतिः — ‘यत्साक्षादपरोक्षाद्ब्रह्म य आत्मा सर्वान्तरः’(बृ. उ. ३ । ५ । १) इति ॥
यस्मादेवं नित्यः अविक्रियश्च आत्मा तस्मात् युध्यस्व, युद्धात् उपरमं मा कार्षीः इत्यर्थः ॥
न हि अत्र युद्धकर्तव्यता विधीयते, युद्धे प्रवृत्त एव हि असौ शोकमोहप्रतिबद्धः तूष्णीमास्ते । अतः तस्य प्रतिबन्धापनयनमात्रं भगवता क्रियते । तस्मात् ‘युध्यस्व’ इति अनुवादमात्रम् , न विधिः ॥ १८ ॥
In plain words
And the unreal — what is that? The thing that cannot stay what it is, that keeps slipping out of its own being. Here is the answer —
When something has an end coming to it, that's what makes it 'finite.' Think of a mirage: the feeling that it's real can go on for a while, but the moment you actually check with a reliable means of knowing, that feeling breaks — that break is its 'end.' Bodies are exactly the same. Like a dream, like a piece of magic, like a body seen in an illusion, the wise call them 'finite' — finite relative to the Self, which is eternal, embodied, holds the body, imperishable, and beyond anything any proof could pin down. And calling the Self both 'eternal' and 'imperishable' in the same breath isn't saying the same thing twice — because in ordinary speech, both 'eternal' and 'destroyed' come in two flavors. A body turns to ash and vanishes — people call that 'destroyed.' But a body can also just change while it's still standing right there — falls sick, wears down — and people call that 'destroyed' too. Naming the Self 'eternal' and 'imperishable' together rules out both kinds of ending at once: neither touches it. Otherwise you'd end up with an eternality like the earth's — lasting a long time, but still shifting underneath. These two words are here precisely so that doesn't happen. And 'beyond any proof' means just what it says: it isn't something perception or any other means of knowing could ever measure or close a fence around.
Here's an objection worth raising: doesn't scripture define who you are? And didn't we just say perception and the other means of knowledge do that too? No — because the Self doesn't need anything to establish it; it's simply given, standing on its own. You only go hunting for a means of knowing once the knower is already there as settled fact. Nobody first fails to know 'I am' and only afterward sets out to pin down some object in the world — that never happens. And nobody, anywhere, finds the word 'Self' unfamiliar. Scripture really is the final word here, but notice what it actually does: it doesn't hand you some brand-new fact about yourself. It strips away what you'd wrongly heaped onto yourself. That's the whole job — not informing you of something you never knew, but clearing away what was never really yours. As the scripture itself says: 'That Brahman which is directly present, immediate, the Self, the innermost reality of everyone' (Bṛhadāraṇyaka Upaniṣad 3.5.1).
Because the Self is eternal, because nothing can alter it — fight. Do not step back from the battle. That is the meaning.
Look closely at what's actually happening in this verse: Krishna isn't issuing a command to go fight. Arjuna is already standing on the battlefield — what's stopping him is that grief and confusion have frozen him into silence. So all the Lord does here is clear that block out of the way. Which is why 'fight' isn't an order from outside — it's just naming what was already true before grief got in the way.
Close to the Sanskrit
But what, then, is that unreal, which goes astray from its own self-existence? — thus it is said —
That in which an end, that is destruction, exists — those are 'having an end.' Just as, in the case of a mirage and the like, the notion 'this is real,' though it persists, is cut off at the end of investigation by a means of valid knowledge — that is its 'end'; so too these bodies, like a dream, an illusion, an illusion-body and the like, are said by the discerning to be 'having an end' — relative to the eternal, embodied, body-possessing, imperishable, unknowable-by-valid-means Self. Such is the meaning. 'Eternal' and 'imperishable' [in the verse] are not redundant, because eternality and destruction are each of two kinds in ordinary usage. As when a body, having become ashes and gone out of sight, is said to be 'destroyed.' And also, even while it still exists, when it has become otherwise transformed, afflicted with disease and so on, it too is said to be 'destroyed.' There, 'eternal' and 'imperishable' mean that it has no connection with destruction of either kind — such is the meaning. Otherwise, like earth and the rest, the Self would have [only relative] eternality; that this should not occur, he says 'eternal,' 'imperishable.' 'Unknowable [by valid means]' means not an object of knowledge, that is, not to be delimited by direct perception and the other means of valid knowledge — such is the meaning.
Objection: the Self is delimited by scripture, and previously also by direct perception and the like. [Reply:] No; because the Self is established by itself. For when the Self, as the knower, is [already] established, the search for a means of valid knowledge arises for one who wishes to know [something else]. Indeed, no one, without first having known the Self as 'I am thus,' afterward proceeds to the ascertainment of an object of knowledge. Nor, indeed, is the Self, by name, unfamiliar to anyone. But scripture is the final means of knowledge; it attains the status of a means of knowledge with respect to the Self solely by way of removing the superimposition of what does not belong to it, not by way of making known an object that was [otherwise] entirely unknown. And thus the Shruti says: 'That Brahman which is direct, immediate, the Self which is the inner Self of all' (Bṛhadāraṇyaka Upaniṣad 3.5.1).
Since thus the Self is eternal and without modification, therefore fight; do not make a withdrawal from the battle — this is the meaning.
For here the obligatoriness of fighting is not being enjoined; rather, this one, already engaged in the battle, sits in silence, bound by grief and delusion. Therefore the mere removal of his obstruction is being effected by the Lord. Hence '[you] fight' is a mere restatement, not an injunction.