Darwin's answer to the question of the origin of species was, in a general sense, that species were descended from other species. Moreover, the family tree of life is a branching one, which means that more than one modern species can be traced back to one ancestral one. For instance, lions and tigers are now members of different species, but they have both sprung from a single ancestral species, probably not very long ago. This ancestral species may have been the same as one of the two modern species; or it may have been a third modern species; or maybe it is now extinct. Similarly, humans and chimps now clearly belong to different species, but their ancestors of a few million years ago belonged to one single species. Speciation is the process by which a single species becomes two species, one of which may be the same as the original single one.
The reason speciation is thought to be a difficult problem is this. All the members of the single would-be ancestral species are capable of interbreeding with one another: indeed, to many people, this is what is meant by the phrase 'single species'. Therefore, every time a new daughter species begins to be 'budded off', the budding off is in danger of being frustrated by interbreeding. We can imagine the would-be ancestors of the lions and the would-be ancestors of the tigers failing to split apart because they keep interbreeding with one another and therefore staying similar to one another. Don't, incidentally, read too much into my use of words like 'frustrated', as though the ancestral lions and tigers, in some sense, 'wanted' to separate from each other. It is simply that, as a matter of fact, species obviously have diverged from one another in evolution, and at first sight the fact of interbreeding makes it hard for us to see how this divergence came about.
It seems almost certain that the principal correct answer to this problem is the obvious one. There will be no problem of interbreeding if the ancestral lions and the ancestral tigers happen to be in different parts of the world, where they can't interbreed with each other. Of course, they didn't go to different continents in order to allow themselves to diverge from one another: they didn't think of themselves as ancestral lions or ancestral tigers! But, given that the single ancestral species spread to different continents anyway, say Africa and Asia, the ones that happened to be in Africa could no longer interbreed with the ones that happened to be in Asia because they never met them. If there was any tendency for the animals on the two continents to evolve in different directions, either under the influence of natural selection or under the influence of chance, interbreeding no longer constituted a barrier to their diverging and eventually becoming two distinct species.
