Reincarnation is the process by which the spiritual essence of any individual (commonly called "the soul") passes from one body to another in a repeated cycle of birth and death.
In the Bhagavad-gita this process is explained using the following analogy: "As the embodied soul passes, in this body, from boyhood to youth to old age, the soul similarly passes into another body at death. A sober person is not bewildered by such a change." (Bhagavad-gita 2.13)
Because the soul eternally exists then this process, if unchecked, is also eternal. In everyday life there is always some degree of distress and suffering & because the soul is eternal, as long as he is in the cycle of reincarnation, then he will be eternally suffering. The Hare Krishna philosophy explains how one can break this cycle of repeated suffering. This is exemplified in the Bhagavad-gita which, in essence, is an explanation of how to break this cycle and achieve liberation.