Species, speciation... and definitions

We can define a specie as organisms that are able to interbreed successfully and produce viable offspring, meaning that their offspring are fertile and can interbreed with other members of the same species.

So what happens if a population of a specific species is geographically separated? or if part of the population preferred a specific food, mating behavior, or adaptation while the rest of the population had a different preference even though the two groups are found in the same location? 

These ⬆ are examples of how speciation may occur. Speciation is when one species diverges into a different specie resulting in two different species that cannot successfully interbreed or produce viable offspring.