A species becomes extinct when the last living individual of that species dies. An extinct species is a lost species - there are no more living examples of the species in existence.
If a species has only a few living members left, and those members are all in captivity (such as in aquariums or zoos), the species is referred to as 'extinct in the wild'.
Species which have relatively few living members are referred to as an endangered species. The species is 'in danger' of becoming extinct.
Species which have a low number of living members are sometimes referred to as threatened or vulnerable species.
The International Union for the Conservation of Nature (IUCN) maintains a website (linked below) which has examples of many threatened, endangered and recently extinct species.