A fossil is any evidence of ancient life, this can mean anything from bone fragments to leaf impressions.
Every fossil is unique because of the variation in living organisms and those of fossilisation. The odds against fossilisation are millions to one, although some animals and plants increase their chance of being fossilised by living in certain places (eg. burrowing in sediment, living in large groups or living in certain areas of the sea).
Even if they do become buried quickly after death the chemical and physical conditions as the sediment turns to rock may be too harsh to preserve fossils. If after all this fossils are preserved, the rock containing them may remain many kilometres below the surface, not to be exposed for millions of years to come.
It is for these reasons that fossils are relatively rare, but if the conditions are right for preservation fossils can be preserved in large numbers and in great detail.