Richard Dawkins has written many detailed, accessible books about this topic, but if I had to pick one, it would be The Ancestor's Tale.

It follows human evolution backwards through time, telling "tales" of various other animals as they join us at different milestones on the journey.

It gave me an appreciation for my place in the grand family tree of life, and is packed with interesting anecdotes about how various features might have evolved.

It would be a great first Richard Dawkins book.