Who is a guru? (gītā 2.5)

Who is a guru? arjuna describes a guru as a mahānubhāva, a person marked by greatness.

gūrūn ahatvā hi mahānubhāvān 2.5

and the commentaries further describe the experiences that gurus should possess.

mahān anubhāvaḥ śrutādhyayana-tapa-ācārādi-nibandhanaḥ prabhāvaḥ yeṣāṁ tān .. (gūḍhārthadīpikā)

mahān anargalo’nubhāvaḥ dharma-brahma-viṣayako bodho yeṣāṁ, tān mahānubhāvān .. (tātparya-bodhinī)

They have studied the scriptures, performed tapas, and practice what they preach. They have had the complete unfettered experience of dharma and the self.

It isn’t overly useful to use guru-lakṣaṇa to test a guru, since we get what our pūrva-karma-saṁskāra dictates. On the other hand, we can use these lakṣaṇas to guide our daily life, i.e. we can perform śrutādhyayana, tapas, and lead a life of virtuous conduct.

The commentator madhusūdana-sarasvatī sees an additional opportunity to eulogize the guru, and plays some sanskrit games. He optionally reads himahānubhāvān as a single word.

himaṁ jāḍyam apahanti iti himahā ādityo’ginrvā, tasyaiva anubhāvaḥ sāmarthyaṁ yeṣāṁ tān .. (gūḍhārthadīpikā)

gurus are himahās, the destroyers of cold, or insentience. Just as the sun, or fire can destroy the cold, a guru can destroy the ignorance of the self.

In the same verse, arjuna goes on to call the guru an arthakāma --

hatvā'rthakāmāṁstu gurūn (2.5)

and svāmi śaṁkarānanda elucides this as someone who instructs his disciples in dharma and the puruṣārthas, which culminate with mokṣa --

arthān dharmādipuruṣārthān śiṣyebhyaḥ kāmayanti bodhayanti iti arthakāmāḥ, tān (tātparya-bodhinī)

All of us can and should strive to be mahānubhāva. Due to the guru-śiṣya relationship, on the other hand, it is the guru alone who is the himahānubhāva, or the arthakāma.