A physical barrier divides a population of a species.
This could be something like a river that changed course, splitting the population in two.
This means half are on one side, and half are on the other, and they CANNOT interact.
Mutations in the DNA cause new features.
Since as the two groups cannot interact, these mutations are different on either side.
Natural selection occurs.
This means that the new features of benefit get spread through the populations on either side.
The conditions on both sides are slightly different, and therefore, the features considered beneficial would also be different.
Eventually, the features on both sides will be so different from each other that they won't be able to interbreed to produce fertile offspring.
This means they have become reproductively isolated, and are two new species entirely.