The picture at the top allows for two important points, the first is that the fossil record shows transitional species. Someone asked me to show transitional species from bacteria all the way up to human beings. As you look through older sets of rocks the species are there. Precambrian rocks show only single cell critters, Cambrian rocks show somewhat larger and more complex plants and animals. Everyone here knows the rest of the story. Someone once said that a beautiful elegant theory can be wrecked by a single ugly fact. If somebody was to produce a fossil showing human footprints alongside Trilobites, or a spearpoint embedded in a T-Rex skeleton, evolutionary theory would fall down in an instant. So far it hasn't happened. The second point is that the diagram is terribly misleading because it looks like a ladder. in fact each of those horse progenitors had several descendants. The diagram should look much more like a bush or a cobweb than a ladder.
One final story, as a kid one of my favorite prehistoric creatures was the Dimetrodon, I always thought the sail fin was really cool. But what was even cooler was a new trait that makes the Dimetrodon one of the more significant "transitional species" It was the first creature to sport multiple types of teeth. Before Dimetrodon came along animals had either sharp pointy teeth or dull crushing teeth. Even though this really neat sail backed beast was clearly not a mammal, it was one of the first steps along the way, it is likely that the fossilized creature above is a distant ancestor of all of us reading my blog today.