Every Sanskrit word has got elaborate meaning. Gṛhastha means one who stays in gṛha, in house. He is called gṛhastha. So can any one living in house be called gṛhastha ? No. Śāstra says, na gṛhaṁ gṛham ity āhuḥ: “Simply a house is not gṛha.” There must be the housewife. Gṛhiṇī gṛham ucyate. In Hindi this word is used, garvāli means if there is no wife, that is not gṛha. And Cāṇakya Paṇḍita says, putra-hīnaṁ gṛhaṁ śūnyam. “You have got wife, but if you have no children, that gṛha is also void.” So gṛhastha (real householder or married person) means to live with wife and children, and cultivating spiritual life. That is called gṛhastha. It doesn’t matter if one lives with wife and children, or if one leads his life has an unmarried – brahmacārī or sannyāsī. Therefore there are so many divisions of life. One can accept whichever status of life is suitable. Brahmacārī, gṛhastha, vānaprastha, sannyāsa āśrama. When the word āśrama is added, that means it has got reference with cultivation of spiritual life. So gṛhastha-āśrama. One can live at home with wife and children, but the business should be Kṛṣṇa consciousness. We don’t accept the artificial renunciation like Māyāvādī sannyāsī – because there is no Kṛṣṇa consciousness and give up this world. Simply by becoming sannyāsī… Brahma satyaṁ jagan mithyā: “This world is false. Brahman is truth. So I give up this world.” That kind of sannyāsī we do not accept. Either one becomes gṛhastha or sannyāsī or brahmacārī, there must be Kṛṣṇa. Then it will be called āśrama. Gṛhastha-āśrama, sannyāsa-āśrama, brahmacārī-āśrama. Therefore the word āśrama is added.
Ref >> Srila Prabhupada Vani.