David,
This is certainly a difficult area for most people in regard to understanding Buddhism. As with most Eastern philosophies and religions, Buddhism does not view death as the final end of phenomena. In Buddhism, only nibbana is said to be the final end of phenomena in regards to the arising and passing away of beings (AN 10.58). According to the teachings on dependent origination, if there are sufficient conditions present, those conditions with inevitably result in future births (SN 12.35). Along with consciousness, craving plays a vital role in the renewal of beings and the production of future births.
To illustrate how craving could result in future births, the Buddha used a simile in which he compared the sustenance of a flame to that of a being at the time of death. Essentially, a flame burns in dependence on its fuel, and that fuel sustains it. When a flame burns in dependence on wood, for example, the wood sustains that flame. However, when a flame is swept up and carried away by the wind, the fuel of wind sustains that flame until it lands upon a new source of fuel. In the same way, a being at the time of death has the fuel of craving as its sustenance (SN 44.9).
The last consciousness of a being at the time of death, with the presence of craving, is the cause for the arising of a new consciousness. In the human realm, this would be in combination with the union of a healthy sperm and egg, although the Buddha often mentioned various other forms of birth in other realms of existence—none of which are free from suffering. Hence, the Buddha states, “Wherever there is a basis for consciousness, there is support for the establishing of consciousness. When consciousness is established and has come to growth, there is the production of renewed existence” (SN 12.38).
Jason