As Śrīla Bhaktisiddhānta Sarasvatī Ṭhākura explains, the word bahirmukha refers to a person who is very busy tasting material enjoyment. Such a person always poses himself as an enjoyer of the external energy of the Supreme Personality of Godhead. Being attracted by external opulence, the nondevotee always forgets his intimate relationship with Kṛṣṇa. Such a person does not like the idea of becoming Kṛṣṇa conscious. This is explained by Śrīla Prahlāda Mahārāja in Śrīmad-Bhāgavatam (7.5.30-31):

matir na kṛṣṇe parataḥ svato vā
mitho 'bhipadyeta gṛha-vratānām
adānta-gobhir viśatāṁ tamisraṁ
punaḥ punaś carvita-carvaṇānām

na te viduḥ svārtha-gatiṁ hi viṣṇuṁ
durāśayā ye bahir-artha-māninaḥ
andhā yathāndhair upanīyamānās
te 'pīśa-tantryām uru-dāmni baddhāḥ

Materialists who are overly attracted to the material body, material world and material enjoyment, who cannot control their material senses, are carried to the darkest regions of material existence. Such people cannot become Kṛṣṇa conscious, either by themselves or by congregational effort. Such people do not understand that the goal of life for a human being is to understand the Supreme Personality of Godhead, Viṣṇu. A human life is especially meant for this purpose, and one has to go through all kinds of penances and austerities and set aside the propensity for sense gratification. Materialists always remain blind because they are always guided by blind rascals. A materialistic person considers himself free to act as he likes. He does not know that he is rigidly controlled by the stringent laws of nature, nor does he know that he has to transmigrate from one body to another and perpetually rot in material existence. Such rascals and foolish people are lured by the prayers of their foolish leaders for sense gratification, and they cannot understand what is meant by Kṛṣṇa consciousness. The material world exists outside the spiritual sky, and a foolish materialist cannot estimate the extent of this material sky. What, then, can he know of the spiritual sky? Materialists simply believe their imperfect senses and do not take instructions from the revealed scriptures. According to Vedic civilization, one has to see through the authority of the revealed scriptures. Śāstra-cakṣuḥ: one should see everything through the medium of the Vedic literature. In this way, one can distinguish between the spiritual world and material world. Those who ignore such instructions cannot be convinced of the existence of the spiritual world. Because they have forgotten their spiritual identity, such materialists take this material world as the all in all. They are therefore called bahirmukha.