Extinction is when a species dies out completely. It could be argued that it can occur before that, say, if there are only males or females left in a sexually reproducing species, or if the remaining pairs are geographically isolated preventing mating.
Over the history of the earth, many more species have become extinct than have existed at any one time. Sometimes a species is replced by descendants that have altered their form enough not to be considered the same species anymore. An example of this is the history of the modern horse, which has descended through a series of distinct, and now extinct, precursor species.