In plain words
It cannot be cut, burned, wetted, or dried. It is eternal, all-pervading, stable, unmoving, and ever the same.
Word for word
This [one] is uncuttable, this [one] is unburnable, unwettable and undryable too; eternal, all-pervading, firm, unmoving is this [one], primeval.
The commentators
Bhagavadgītābhāṣyam
यतः एवं तस्मात् —
यस्मात् अन्योन्यनाशहेतुभूतानि एनमात्मानं नाशयितुं नोत्सहन्ते अस्यादीनि तस्मात् नित्यः । नित्यत्वात् सर्वगतः । सर्वगतत्वात् स्थाणुः इव, स्थिर इत्येतत् । स्थिरत्वात् अचलः अयम् आत्मा । अतः सनातनः चिरन्तनः, न कारणात्कुतश्चित् निष्पन्नः, अभिनव इत्यर्थः ॥
नैतेषां श्लोकानां पौनरुक्त्यं चोदनीयम् , यतः एकेनैव श्लोकेन आत्मनः नित्यत्वमविक्रियत्वं चोक्तम् ‘न जायते म्रियते वा’(भ. गी. २ । २०) इत्यादिना । तत्र यदेव आत्मविषयं किञ्चिदुच्यते, तत् एतस्मात् श्लोकार्थात् न अतिरिच्यते ; किञ्चिच्छब्दतः पुनरुक्तम् , किञ्चिदर्थतः इति । दुर्बोधत्वात् आत्मवस्तुनः पुनः पुनः प्रसङ्गमापाद्य शब्दान्तरेण तदेव वस्तु निरूपयति भगवान् वासुदेवः कथं नु नाम संसारिणामसंसारित्वबुद्धिगोचरतामापन्नं सत् अव्यक्तं तत्त्वं संसारनिवृत्तये स्यात् इति ॥ २४ ॥
In plain words
Because this is how it stands, therefore —
Nothing that destroys anything else -- not a blade, not fire, not anything -- can touch this Self. That's exactly why it's eternal. And because it's eternal, it's everywhere, filling everything without exception. And because it's everywhere, it can't be moved from anywhere -- it's fixed, stable, like a deep-rooted post. And because it's stable, it never budges at all. Which is why it's called ancient beyond ancient: it was never produced by any cause, was never new to begin with.
You might notice these verses seem to repeat themselves, and wonder why. Here's why: one single verse already said everything -- that the Self is eternal, that it never acts. So anything said here doesn't add new content, it just says the same truth again, sometimes in the same words, sometimes in different ones. But that's exactly the point. The nature of the Self is genuinely hard to grasp, so Krishna keeps circling back to it, saying the same one truth in fresh language each time. Because think about what happens otherwise: if it's stated only once, a mind still caught in the cycle of birth and death can nod along, file it away as an interesting idea -- 'oh, so I'm not really bound by all this' -- without it ever actually landing. And an idea that just sits there as a belief can't free anyone from anything. So he says it again, and again, in different words, until it stops being a concept you hold and becomes something you actually see.
Close to the Sanskrit
Since thus, therefore —
Because things that are mutually the cause of [each other's] destruction -- swords and the like -- are not able to destroy this Self, therefore it is eternal. Because it is eternal, it is all-pervading. Because it is all-pervading, it is like a fixed post, that is, 'stable.' Because it is stable, this Self is immovable. Therefore it is 'primordial' -- ancient, not produced from any cause whatsoever -- meaning, not newly arisen.
The redundancy of these verses should not be objected to, because by one single verse alone the eternality and actionlessness of the Self were already stated -- by [the words] 'is not born, nor does it die' and so on [Bhagavad Gita 2.20]. In that regard, whatever is said here concerning the Self does not go beyond the meaning of that [same] verse; it may be redundant in wording in some respects, redundant in meaning in others. Because the reality of the Self is difficult to understand, having brought up the topic again and again, the Lord Vasudeva expounds that same reality through different words -- [with the thought]: how indeed could the unmanifest reality, having merely fallen within the notion 'not-transmigratory' held by those [still] bound in transmigration, [thereby actually] serve for the cessation of transmigration?