All the three precepts of spirituality moksha karma and reincarnation can be best understood indulging in Indian spirituality as detailed in Bhagavad Gita.
Initially we need to understand that we are primarily a spirit, consciousness existing in cosmos that needs gaining absolute purity again. No sooner life supporting planets like mother earth evolved, the encircling souls’ atmans immediately start manifesting a body on mother earth. The journey of life for a soul atman on mother earth starts with amoeba (the first manifestation) by a soul atman.
Does it mean before manifesting human body, we were at a time an amoeba… yes, Indian spirituality says so!
The earthly journey of soul atman further evolves into multi-cell formation, insect life, plant life animal and then finally human form. It is only in human form a soul atman finally regains release from cycle of birth and death forever. Enlightenment, Mukti could never be gained by lower forms of life. Becoming a pure soul atman was possible only in human form.
After death of present body the released soul atman again manifests a new body to continue cosmic journey of life. This cyclic cosmic journey of life continues unabated manifestation after manifestation, body after body. This crux of life of manifesting body after body is termed reincarnation, rebirth in Hinduism and also Jainism.
And why does a soul atman need manifesting body after body?
In their cosmic sojourn the pure soul atman gains impurities similar as a rolling ball gathers moss. To cleanse self of dross impurities within starts earthly life cycle of every soul atman. By itself no soul atman could purify self. It needs a medium, a body to do so. When the soul atman takes a human body, it indulges in karma. Karma is the process through which a soul atman could cleanse self of dross impurities within.
As long as a single trace of dross impurity remains in a soul atman, it keeps indulging in karma to purify itself. Indulgence in karma by human beings and all lower forms of life was never a matter of choice. Everyone indulges in karma knowingly or unknowingly. As per Bhava karma doctrine of Jainism every single thought precipitates into an act of karma. We may or may not want to indulge in karma but subconsciously we all the time indulged in karma.
It is through the complex process of karma life evolves in cosmic system. In absence of karma, no soul atman could purify self. All would become stagnant, decay and die.
To indulge in karma, to gain absolute purity forever every soul atman enters cycle of reincarnation rebirth. Indulging in Indian spirituality when human beings finally gained enlightenment, after death of mortal body one reaches state of moksha salvation forever! Moksha cannot be reached bodily; it is always attained after mortal death of an enlightened one.
The leaving of mortal frame by an enlightened one is termed moksha salvation, Mukti from cycle of birth and death forever.
Summarizing it all, for human beings to reach state of enlightenment and finally moksha our indulgence in spirituality as detailed in Bhagavad Gita and Upanishads (independent spiritual treatises) is necessitated.