The idea of rebirth or life after death seems common to the major religions, I suspect for two main reasons. The first being that two thousand odd years ago people’s understanding about physics, biology etc were limited and it was easy for them to imagine continuing after death. Polytheism and Animism were rife, and so if rocks and trees had spirits, why not dead people?
So ingrained was the idea in the cultures of the time that spritual teachers were more or less obligated to include the idea in their teaching in order to be accepted at all.
Secondly, the idea makes a termendous metaphor for spiritual growth. In most religions there is some sort of discrimination between a good place and a bad – heaven and hell. The implication being that following a period of great change you can aim to end up in one or two states – a pleasing and fulfilling one, or a vicious and hurtful one.
Buddhism offers a different slant in that the goal (as such) of Buddhism is to achieve Nirvana which rather than guaranteeing you rebirth in some pleasant domain does almost the reverse – by aiming to achieve a blissful state which is said to free you from being reborn.
In this sense it is about breaking the round cycle of existence – from your self being reborn in every instant into the same set of traps (hatred, craving, aversion). Each moment you break the chain by having an experience and not entertaining feelings of craving or aversion, you break that cycle and are liberated from it.
This applies literally to just about every moment we experience, just as the metaphor applies to the endless round of lifetimes.