The book is in four sections. The first, 'Stars in Your Eyes' is based on Barrow's own subject of cosmology, and includes the COBE microwave spectrum and Supernova 1987A. The second section 'Spatial Prejudice' deals with a variety of subjects - space travel, maps and microscopic imagery. The third section 'Painting by Numbers' looks at mathematical images - powerful computers have led to plenty of these, for instance the Mandelbrot set, but the book also looks at more traditional mathematics such as the Platonic solids. 'Mind over Matter' is the final section, and includes pictures from physics and chemistry, such as Feynman diagrams and the periodic table.
The book is written in a non-technical way, and the chapters are short and easy to read. Sometimes it helps to have a bit of a background in the subject but it isn't vital. It's very much a 'coffee table book' but it's a very good one, which you or your children will enjoy browsing, and may be inspired to follow up on one of the topics using the extensive notes at the end.
(Note: the hardback is a bit too heavy to hold comfortably so you might want to consider waiting for the paperback instead)