Sympatric speciation is the process through which new species evolve from a single ancestral species while inhabiting the same geographic region.
It involves the splitting of an ancestral species into two or more reproductively isolated groups without geographical isolation of those groups. The key aspect of sympatric speciation is that it occurs when incipient species are in physical contact with each other, potentially able to interbreed and exchange genes.
It is one of the three traditional geographical modes of speciation. Here there is no geographical constraint to interbreeding. Sympatric speciation is unique because the process begins with complete genetic mixing between the diverging groups.
Sympatric speciation events are quite common in plants, which are prone to acquiring multiple homologous sets of chromosomes resulting in polyploidy.
The speciation is the fact that two different populations of a same specie leads to 2 news species.
Allopatric speciation can occurs when populations of a same specie are geographically separated, so genetics exchanges are not possible any longer.By living in different places, they have to face different environmental conditions (heat, salinity, pH ...) and so to adapt differently. Becoming slightly differently generation by generation, they will become so different that they won't be able to breed if they were in the same place again.
The Darwin's finches are a good example of allopatric speciation !