The Buddha remembered his past lives. Even today there are monks, nuns and others who can remember their previous existences. Such a strong memory is a result of deep meditation and mental training. For those who can recall their past lives, the idea of rebirth becomes an established fact which puts this present life in a meaningful perspective.
The law of karma can only be fully understood in the framework of many lifetimes, sometimes it takes this for kamma to bear its fruit.
Rebirth is not limited merely to the human realm. The Buddha taught that the realm of human beings is but one among many. In addition there are realms of heavens, hells, animals and ghosts. Depending on the kamma one has accumulated, one may be reborn into any of these. Understanding this brings up a sense of empathy and respect for the lives of all beings.
Because no realm is permanent, the repetitive cycle of birth and death and the wandering on from realm to realm is inherently unsatisfying. Eventually one seeks a way out.
By following the Noble Eightfold Path to its culmination of enlightenment, the process of rebirth ceases completely.