In plain words
Jñāna, the object known, and the knower form the threefold impulse to action; instrument, object, and agent form the threefold constituents of action.
Word for word
Knowledge, the known, the knower: the threefold impulse to action; instrument, object, agent: thus the threefold basis of action.
ज्ञानं ज्ञेयं परिज्ञाता त्रिविधा कर्मचोदनाकरणं कर्म कर्तेति त्रिविधः कर्मसङ्ग्रहः
Other commentaries
The commentators
▸Bhagavadgītābhāṣyam
अथ इदानीं कर्मणां प्रवर्तकम् उच्यते —
ज्ञानं ज्ञायते अनेन इति सर्वविषयम् अविशेषेण उच्यते । तथा ज्ञेयं ज्ञातव्यम् , तदपि सामान्येनैव सर्वम् उच्यते । तथा परिज्ञाता उपाधिलक्षणः अविद्याकल्पितः भोक्ता । इति एतत् त्रयम् अविशेषेण सर्वकर्मणां प्रवर्तिका त्रिविधा त्रिप्रकारा कर्मचोदना । ज्ञानादीनां हि त्रयाणां संनिपाते हानोपादानादिप्रयोजनः सर्वकर्मारम्भः स्यात् । ततः पञ्चभिः अधिष्ठानादिभिः आरब्धं वाङ्मनःकायाश्रयभेदेन त्रिधा राशीभूतं त्रिषु करणादिषु सङ्गृह्यते इत्येतत् उच्यते — करणं क्रियते अनेन इति बाह्यं श्रोत्रादि, अन्तःस्थं बुद्ध्यादि, कर्म ईप्सिततमं कर्तुः क्रियया व्याप्यमानम् , कर्ता करणानां व्यापारयिता उपाधिलक्षणः, इति त्रिविधः त्रिप्रकारः कर्मसङ्ग्रहः, सङ्गृह्यते अस्मिन्निति सङ्ग्रहः, कर्मणः सङ्ग्रहः कर्मसङ्ग्रहः, कर्म एषु हि त्रिषु समवैति, तेन अयं त्रिविधः कर्मसङ्ग्रहः ॥ १८ ॥
In plain words
Now, here, what sets action in motion is named —
'Knowledge' means simply that by which one comes to know — spoken of here without restriction, as covering every object there is. Likewise 'the knowable', what is to be known, is spoken of just as broadly, covering everything. And likewise, 'the knower' is the Self as conditioned by a limiting adjunct — a construct of ignorance — also called 'the experiencer'. This triad, unrestricted in scope, is what sets every action in motion; being threefold, it is the very impulse behind action. Because once these three — knowledge and the rest — converge, aiming at either taking hold of something or letting it go, every action gets underway. Then this whole convergence, begun by the five factors — the substratum and the rest — gets sorted by whether its base is speech, mind, or body, consolidated into three, and gathered under three headings: instrument and the rest. Here is what that means: 'the instrument' is that by which one acts — external, like hearing and the other senses; or internal, like intellect and the other faculties. 'The object' is what the agent most wants, that which the action reaches and affects. 'The agent' is the one who deploys the instruments — again characterized by a limiting adjunct. This threefold grouping is called 'the summation of action' — 'summation' because things are gathered into it; the summation, specifically, of action. Since action, in every sense, is fully comprehended within these three, this 'summation of action' is rightly called threefold.
Close to the Sanskrit
Now, at this point, that which sets actions in motion is stated —
'Knowledge' — 'by which one knows' — thus, is spoken of, without distinction, as having everything as its object. Likewise, 'the knowable', that which is to be known — that too is spoken of, only in a general sense, as everything. Likewise, 'the knower' — characterized by a limiting adjunct, imagined by ignorance, the experiencer. Thus this triad, without distinction, is the instigator of all actions, threefold, of three types — the impulsion to action. For, indeed, when these three — knowledge and the rest — converge, having as its purpose rejection, acceptance, and so on, the undertaking of all action would occur. Then, begun by the five, the substratum and the rest, by the distinction of the locus being speech, mind, or body, consolidated into three, it is subsumed among the three — instrument and the rest — this much is said. 'The instrument' — 'that by which one acts' — thus: external, hearing and the rest; internal, intellect and the rest. 'The object' is most desired by the agent, being pervaded by the action. 'The agent' is the director of the instruments, characterized by a limiting adjunct. Thus, threefold, of three types, is 'the summation of action' — 'is gathered in this', thus, is 'summation'; 'the summation of action' is the summation of action. For, action indeed is comprehended within these three; therefore, this 'summation of action' is threefold.