Charles Darwin's original suggestion was that natural selection would cause a species to change, and then change more, and more, and more.
This was 1859, and we didn't learn about DNA until 1948. So, Darwin wasn't quite clear about what was going on "under the hood". But he did know about artificial selection. He was aware of how mankind had created dog breeds, and he himself was a pigeon breeder.
So, he did have a clear idea about what intermediate creatures would look like. Suppose we started with some animals that are 3' high. But of course they aren't all exactly 3' high. Perhaps they vary from 2.5' to 3.5'. Suppose there is selection pressure to become taller - perhaps so they can see further over tall grass.
They don't instantly get taller. In the long term, and on the average, the shorter individuals have fewer children. After a while, the average is up to 3.5'. There are still some that are 3' high, but they are now "short" instead of "average". Many generations later, the average is up to 4', and "short" is 3.5'. But there was never a moment when the children were freakish - when the children looked unusual to their parents. The average height might have crept up by a hundredth of a foot per generation, or perhaps a thousandth per generation. It could be that slow because there is also a pressure to be short. Perhaps the smaller creatures survived droughts better, or lived longer.
Today, we know that most species are like dogs in having an amazing amount of variability in their genetic information. This means that a considerable amount of apparent change may be required before two groups cease to be interfertile. So, the traditional scenario is likely to just be a prelude to one of the other speciation scenarios. Perhaps the two groups will just cease to meet, because one hides in holes, and the other under fallen trees. Perhaps a wasp will start to live on two different plants, and matings will only happen between individuals who agree on a preference for one or the other food. And so on. In short, Darwin's scenario is not normally enough, in and of itself.