Paraṁ dhāma means He is the supreme rest of everything. And pavitram. Pavitram means He is pure from material contamination. And He's addressed as puruṣam. Puruṣam means the supreme enjoyer: śāśvatam, śāśvata means from very beginning, He's the first person: divyam, transcendental: devam, the Supreme Personality of Godhead: ajam, never born: vibhum, the greatest.
Now, one may doubt, that because Kṛṣṇa was the friend of Arjuna, therefore he might say all these things to his own friend. But Arjuna, just to drive out this kind of doubts in the mind of the readers of Bhagavad-gītā, he establishes his proposition by the authorities.
He says that Lord Śrī Kṛṣṇa is accepted as the Supreme Personality of Godhead not only by himself, Arjuna, but He is so accepted by authorities like Nārada, Asita, Devala, Vyāsa. These personalities are great personalities in distributing the Vedic knowledge, accepted by all ācāryas.
Therefore Arjuna says that "Whatever You have spoken so far to me, I accept them as completely perfect." Sarvam etad ṛtaṁ manye (BG 10.14): "I take it, I believe it that whatever You have spoken, they are all right. And Your personality, Your personality of Godhead, is very difficult to understand. And therefore You cannot be known by even the demigods. You cannot be known even by the demigods." That means the Supreme Personality Godhead cannot be known even by greater personalities than the human being. And how a human being can understand Śrī Kṛṣṇa without becoming His devotee?
Therefore Bhagavad-gītā should be taken up in a spirit of devotee of Lord Śrī Kṛṣṇa. One should not think that he is equal, on the same level of Śrī Kṛṣṇa, or one should not think that He is an ordinary personality, maybe a very great personality. No. Lord Śrī Kṛṣṇa is the Supreme Personality of Godhead.