Mukti is a word coined in Hinduism to explain the fundamentals of enlightenment and moksha. Mukti in Hindi stands for liberation in English. The state of Mukti by a human being is reached when indulging in spirituality, sacred texts of Hinduism like Bhagavad Gita human beings finally make it to the end. In simple words, when we as a soul atman reach stage of absolute purity, we need not manifest a human body any further.
This liberation from cycle of manifestations, gaining body after another is termed Mukti.
Spiritually both Moksha and Mukti mean the same. When a soul atman becomes totally liberated from all bondages of earthly life, one reaches the state of Mukti.
From the first manifestation by a soul atman to the last, the effort of every soul atman always remains liberation from cycle of birth and death at the earliest. This becomes a reality when indulging in spirituality human being succeeds gaining enlightenment in their lifetime.
Here we must understand that spirituality as detailed in Hinduism scriptures like Bhagavad Gita needs to be followed. In absence of wisdom contained in Bhagavad Gita, none world over could ever gain enlightenment or Mukti from Samsara (worldly life). All enlightened souls in the entire history of mankind till date succeeded in reaching state of enlightenment only from India (erstwhile Bharatvarsha). Spiritual philosophy is primarily an Indian concept.
The original gist of Bhagavad Gita containing 700 shlokas verses is available from Gita press, Gorakhpur, India along with English transliteration for mere $1 (even less) yet none world over seems interested in travelling path of spirituality as detailed in Bhagavad Gita. Reason being, it is not that easy indulging in Indian spirituality.
One primarily needs becoming a Swami Vivekananda in real life to undertake spiritual journey successfully. Furthermore we must also realize that it is not human body that gains release from cycle of birth and death; it is our consciousness inside our heart that requires so.