In plain words
Know action to arise from Brahman, the Veda, and the Veda from the Imperishable. Therefore the all-pervading Veda is ever established in yajña.
Word for word
Know action [as] having its origin in brahman [the Veda], [and] brahman as arising from the Imperishable; therefore the all-pervading brahman is always established in yajña.
The commentators
Bhagavadgītābhāṣyam
तच्चैवंविधं कर्म कुतो जातमित्याह —
कर्म ब्रह्मोद्भवं ब्रह्म वेदः सः उद्भवः कारणं प्रकाशको यस्य तत् कर्म ब्रह्मोद्भवं विद्धि विजानीहि । ब्रह्म पुनः वेदाख्यम् अक्षरसमुद्भवम् अक्षरं ब्रह्म परमात्मा समुद्भवो यस्य तत् अक्षरसमुद्भवम् । ब्रह्म वेद इत्यर्थः । यस्मात् साक्षात् परमात्माख्यात् अक्षरात् पुरुषनिःश्वासवत् समुद्भूतं ब्रह्म तस्मात् सर्वार्थप्रकाशकत्वात् सर्वगतम् ; सर्वगतमपि सत् नित्यं सदा यज्ञविधिप्रधानत्वात् यज्ञे प्रतिष्ठितम् ॥ १५ ॥
In plain words
And action of this kind — where does it come from? To that, he says:
'Action has Brahman as its source' means: here 'Brahman' means the Veda, and the Veda is exactly what gives rise to, causes, and reveals action — that is what it means for action to have Brahman as its source. And Brahman, in this same sense the Veda, itself has the Imperishable as its source — that Imperishable is Brahman, the Supreme Self, from which the Veda arises. So 'Brahman' here simply means the Veda, that's the whole of it. And because the Veda arises directly from the Imperishable, the Supreme Self, effortlessly, the way a person's breath arises — it is, for that very reason, all-pervading, since it reveals every single thing there is to know. And yet, all-pervading as it is, it still remains eternally, always, centered on sacrifice, because the injunctions concerning sacrifice are what is primary within it.
Close to the Sanskrit
And that action of such a kind — from what has it arisen? — thus he says:
'Action has Brahman as its source' [means]: Brahman [is] the Veda; that [is] the origin, [i.e.] the cause, the revealer, of which [action] — that action, 'having Brahman as its source', know, understand. Brahman, again — [i.e.] the one called the Veda — [has] the Imperishable as its source; the Imperishable [is] Brahman, the Supreme Self, the source of which [the Veda] — that [Veda is] 'having the Imperishable as its source'. 'Brahman' [means] the Veda — such is the meaning. Because, directly from the Imperishable called the Supreme Self, like the breath of a person, Brahman [the Veda] has arisen — therefore, because of [its] revealing all things, [it is] all-pervading; even though all-pervading, [it is] ever, always, established in sacrifice, because of the primacy of the sacrificial injunction [within it].