James - Our ancestors were apelike creatures but were very different from modern apes. One our ancestors gave rise to to both modern humans and moderns apes. The illustration that book attempts to show are different stages of human evolution but obviously the changes between each of those stages was gradual and took place over many 1000's of generation, Each of those generations would have looked just like the previous one, the changes accumulated over time.
Its a bit like looking at photographs of someone at different stages of life - if you looked at photos of a person as a baby, a toddler, a preteen, a teenager a 50 year old and a 90 year old you wouldn't assume that the individual jumped from one stage to another would you? You know that every day gradual changes occur, so subtly that you can not detect those changes day by day. But if you jump forward in time the changes are obvious.
It is the same with the fossil record. The fossils that we have are like "photos" of different stages of the evolution of humans. In effect we have a record of the baby, the toddler, the preteen etc. but we don't have every photo in between. The missing "photos" represent many generations, every generation showing subtle differences that gradually accumulate to create significant changes.