Living books are books written by a single author or a few authors, rather than by committee. Textbooks of the past few decades have been written largely by special interest groups who override the work of even the original authors of the text. These authors all too often never even see the final product. Many such books are rife with error.
Living books may not be error or bias free, but they are as a rule written with a much higher interest level, which will hopefully inspire further reading and study on the subject at hand. The best cure for preventing or overcoming error or bias in a single book is to read from a large variety of authors on a subject.
One may easily determine whether a book qualifies as a "living" book by reading a few pages. If the book is engaging, if the words transport you into the story and/or if there are beautiful photos or illustrations included, then chances are this book will qualify as a living book for your family. Not everyone will have the same tastes in reading material, so even a great classic may not resonate with everyone.
Books that engage readers through strong narrative have a better chance of being remembered and of spurring further learning. A narrative approach to writing about any subject helps set memory pegs which children can latch onto in recalling that information over time. And, best of all, the narrative approach makes learning MORE FUN!