Spiritual aspiration in Hinduism signifies a desire to seek God or the truth about oneself. It is the yearning of the soul for the supreme Spirit. It is a genuine ardour for liberation from the bondage of death-bound transitory existence. Spiritual aspiration is the central propelling force in Hindu religious and spiritual life and alone leads the human mind towards the experience of the Divine. It can also be described as a struggle to raise one’s consciousness, to connect and be in communion with the Spirit, to reach greater heights of personal spiritual progress and evolution. It is essentially a pure and positive emotional fervor, born out of the faculty of discernment, viveka, and detachment, vairagya — and it is yearning for God that makes Hindu religion meaningful.
In Vedantic parlance spiritual aspiration is termed mumukshutva.
The mumukshutva mentioned in the Vedanta literature, the viraha that we find in
bhakti literature, and the vyakulata that we come across in the life of Sri
Ramakrishna, Swami Vivekananda, and other saints — all indicate different
shades of expression of spiritual aspiration.
Aspiration, indeed, is the cry of the inner soul, the jivatman,
for the experience of the supreme Spirit, Paramatman. The prayerful expression
in one of the famous mantras of the Brihadaranyaka Upanishad indicates the
intensity of aspiration of the seeker appealing to the Almighty: Asato ma
sad-gamaya tamaso ma jyotir-gamaya mrityor-ma-amritam gamaya; lead me [O Bhagvan]
from untruth to truth, from darkness to light, from mortality to immortality.’ We
find another fervent prayer in the Isha Upanishad: ‘Tat-tvam pushaannapavriṇu
satya-dharmaya drishtaye; O Sun [supreme Spirit], please remove that [veil of
ignorance] so that I, who am righteous, can experience the Truth.’ Vedantic
literature and other scriptures, throughout, are replete with such impassioned
petitions expressing the aspirations of seekers.
Source – excerpts from article titled 'Aspiration' by Swami Muktidananda published in Prabuddha Bharata January 2010 issue.