Over multiple generations, interbreeding populations gradually change their features as the ongoing process of replication, heritable difference, and natural selection adjusts the surviving population to severe pressures caused by changes in the environment. Adverse pressure can come from any combination of war/predators, disease, starvation/drought, or natural disasters including meteor strike or inevitable large scale climate change, etc.
When overall situations are good, the population breeds and multiplies becoming more heritably diverse in the process. When situations are bad, these pressures become the most severe and the only survivors to seed the next generation will be the few whose heritable differences makes the difference in whether they are 'selected' to live while the masses die. The future generations will thus all be adapted to the the distinct inherited features of the groups survivors and will tend to hold those features even when they are no longer necessary to survive the next inevitable environmental crises.
Darwin's theory states that whenever an interbreeding population is somehow geographically separated into two different groups which can't reconnect to interbreed, each group will thereafter face different environmental challenges and evolve in different ways. This process will continue indefinitely until each group is eventually so different that the two groups will no longer interbred if they ever again come in contact with each other. Once that step occurs, there will no longer be a cross mating to recombine the two groups and the process of evolving into different species will be complete.
I hope this helps...
Then there's been a whole LOTTA separatin' been goin' on over the millineums!