अर्जुन
In plain words
Arjuna said: Out of grace for me, You have spoken the supreme secret called Adhyātma; by Your words this delusion of mine has gone.
Word for word
For favouring me, the supreme secret word named adhyātma which [was] spoken by You: by that this delusion of mine [is] gone.
The commentators
Bhagavadgītābhāṣyam
भगवतो विभूतय उक्ताः । तत्र च ‘विष्टभ्याहमिदं कृत्स्नमेकांशेन स्थितो जगत्’(भ. गी. १० । ४२) इति भगवता अभिहितं श्रुत्वा, यत् जगदात्मरूपम् आद्यमैश्वरं तत् साक्षात्कर्तुमिच्छन् , अर्जुन उवाच —
मदनुग्रहाय ममानुग्रहार्थं परमं निरतिशयं गुह्यं गोप्यम् अध्यात्मसंज्ञितम् आत्मानात्मविवेकविषयं यत् त्वया उक्तं वचः वाक्यं तेन ते वचसा मोहः अयं विगतः मम, अविवेकबुद्धिः अपगता इत्यर्थः ॥ १ ॥
In plain words
The Lord's own manifestations have now been described. And in that connection, having heard the Lord declare, 'Having pervaded and firmly upheld this entire world with a single part of myself, I stand' — Arjuna, longing to see directly that primal, divine reality whose very form is the world itself, spoke —
'To show me grace' means: for the purpose of showing grace to me. 'Supreme' means: unsurpassed, with nothing above it. 'Secret' means: to be guarded, not handed around. 'Called adhyātma' means: having for its subject the discrimination of Self from non-Self. The word, the actual statement, that you spoke — by that word of yours this delusion of mine is gone. The cognition that could not tell Self from non-Self has left. That is the sense.
Close to the Sanskrit
The Lord's manifestations were stated. And in that regard: 'Having pervaded and supported this entire world with one part, I stand' (Bhagavad Gītā 10.42) — thus declared by the Lord; having heard this, wishing to directly see that primal, divine reality whose form is the world itself, Arjuna said —
'For grace to me' — for the purpose of grace to me; 'supreme' — unsurpassed; 'secret' — to be kept guarded; 'named adhyātma' — having as its subject the discrimination of Self and non-Self; that word, that statement, which was spoken by you — by that word of yours this delusion of mine has gone: the non-discriminating cognition has departed. This is the meaning.